I wrote this in answer to a question on the Invicta forums. Mitrans are the most restricted morally; nice to know the boundaries expected.
I shall endeavour to keep this organised as firstly what is known from the books/ingame, secondly interpretations by players.


A
Mitran Mythology, what is known from books/ingame.

Mitra is the supreme deity, standing alone above all other divinities.
He has no pantheon of fellow deities but he does have saints, those who have displayed supremely his virtues during life. [How sainthood is conferred is unknown to me.] People swear by them, and some believe they work miracles.
He does not exist in his idols nor in animals in the world but is immanent, all around.
Mitra does not accept sacrifices of any kind, animate or inanimate. However, monetary donations are certainly accepted for the good works of the faith.
The statues in temples are representations of the human ideal, that is the closest a human can get in envisaging the divine... or are of the saints.
No human can ever know what Mitra actually looks like, but one depiction is as a handsome man with magnificent shoulders, a patriarchal beard, and thick curls of hair confined by a simple band about the temples. Often depicted with book/staff/both or sometimes with a Mitran holy symbol in the right hand and a sword in the left.

Mitrans believe that Mitra will judge them in an afterlife.
There is a heaven and a hell. Men's souls are subject to judgment after death, based upon the kind of lives they led.

Mitran Virtues
Trust, Truth, Honour... these are the virtues Mitra shows us.
Truth and Learning are high ideals
Harm only those that seek to harm you

Some teach that Mitra wants people to forgive their enemies.
Do good works, aiding others.
Donate money to the temples to support the good works the priests do.
Humility
Exorcise the demons and undead
Bury the dead (or on occasion burn or mummify them), do not defile them.

There are Mitran orphanages
Many Mitran healers.
Protection and aid for the weak
There is a high-level of armed self-defence shown, particularly for male priests and saints, with the staff and the sword being the prime weapons chosen.
A civilised person's god, with an emphasis on learning and truth.

Stand to pray before Mitra, do not crawl on your belly as a snake.


Mitrans in the world
Hierarchy of the priesthood - known titles are:
Arch-priest (in a large wealthy city temple)
Father (chief priest in a village temple/chapel)
Brother (assistant or mobile priest)
All the higher priests seem to be male.

In those countries where Mitran worship is widespread (supreme amongst them being Aquilonia), there are major temples, smaller chapels in the same city or town, and chapels of worship in each village... for every person needs to be taught the virtues so that they have their chance to reach heaven by practising them. Static priests assigned to the larger of these chapels.

There are missionary priests as this is a proselytising religion, with some very determined to save the souls of others by bringing them knowledge of the Light of Mitra.

A degree of arrogance is shown by some followers of Mitra, consistent with the belief that Mitra is the god of civilisation, the supreme deity, and his followers a cut above those who worship idols.

It is accepted that other gods exist and it is permitted to worship them in a lesser manner except where such deities oppose Mitra.
Set (lord of darkness and snakes) is the main opposing deity. Mitra fought Set and, according to Mitran theology, defeated him. [I rather imagine this would be celebrated and I suggested 21st December last year... the time when the increasing darkness starts to be pushed back.]

In Aquilonia in the time of King Conan, the Mitrans are no longer able to persecute those that worship other deities, with even priests of Set allowed to talk openly though much derided. Some oppose this loss of status of state-religion; others embrace it.

The worship of Mitra grew rapidly a few centuries ago after the deeds of the sage Epimetreus.

Some Mitran sayings
The Blessing of Mitra follow you
Mitra's grace go with you
Walk in Mitra's Light
Mitra be with you
Mitra go with you
May Mitra protect you
Mitra preserve you
May Mitra guide your blade
Walk in peace
Mitra bless your paths
Let the peace of Mitra wash over you
Peace go with you
Do the Good God's work

Mitran Iconography
The colours associated with Mitra are blue, white and gold. Mixes of colours are most often blue and white or blue and gold. (And as the Lion King, the Crown of Aquilonia in the personage of Conan has a golden lion on a blue background on banners everywhere. [Unsure if the Lion iconography goes further back into the reign of Numedides and before])

Elements associated with Mitra: Light, both sunlight and the light of inspiration/learning. Also Water, mostly in its association with healing.
A secondary association with Plant, for light and water are what raises the crops that sustain humanity.

Symbols:
Rising sun with rays, often atop a staff, or the straight path of honour that leads to the light eternal or the whole forming what could be a mace to smite with or an ever-burning torch of light. The Mitran Holy Symbol
Full sun with rays
Ripening wheat
8-petalled flower
Blue chalice with golden sun within (often shown with a symbolic face above [perhaps Mitra is watching you?])
Book
Scroll
Lion face (in a chapel that seems devoted to the specially revered dead [war heroes perhaps?])
Mirror

Magic:
In the books rare of course, with Mitra regarded as both omniprescent but also so supremely divine as to be beyond full comprehension. There is one statue to Mitra in Khoraja that appears to speak, but Khoraja is far away from Aquilonia and there many other faiths are present, and it could be a priest speaking with trickery from behind a curtain.

Cups of Healing blue-white liquid
Blinding Light
Searing Light
Chains of Condemnation to hold someone while they are forced to think of their transgressions
Purification of Mitra
Manifestation of Mitra - a small head that comes to reinforce healing
Avatar of Mitra - instantly stuns those opposing
Blessing of Mitra and other spells to protect and aid those working with Mitra's priest
Exorcism and other spells against fear, charm, undead, demons
The fatalities for PoMs feature a great beam of light as Mitra judges the one opposing his priest.

Saints
Female saint of healing, portrayed with scroll or cup. Single breast bare, full-length robe. [I named her Saint Agnes of the Healing Hands]
Young male saint, portrayed with spear in right hand, shield with mirror symbol in left. Wears sun-crest helmet and long robe. Pendant or clasp with 8-petalled flower. [perhaps a devotee from more southerly lands or appropriated from a minor deity attendant on Ishtar as he has a more Shemitish look]
Male saint, depicted as strong warrior, leader perhaps. Helmet, armour, 2 handed sword with rolled-scroll symbol on hilt. [Looks very Aquilonian]
Male saint, depicted as older warrior/leader. Sword in right hand, with Mitran Holy Symbol. Helmet tucked under left arm. Breastplate and tasset.
[A couple of saints' names to follow, from fiction by fellow players]

Temples/Chapels
White stone
Semi-circular windows, the shape of the rising sun
Plain altar on a dais
Braziers, lit during worship
Sacral wine
Offering plate
Sometimes a pool
Decoration with some or all of the symbols of Mitra

In addition, larger temples have some or all of the following:
Steps up to entrance, reaching to the light of the sky
Golden dome, of the sun
Sweeps of lit braziers marking entrance
Large pools
Statues of Mitra and the saints
Statues of seated bare-chested females with swords on their laps


Lapses of faith
From the quests and sayings in game one can see that there is room for a Mitran priest to be human and frail yet the ideals are pretty high. Arrogance, a disinclination to get dirty, hypocrisy, greed, bigotry are displayed at various points. Though truth is a virtue, misleading is practised by some eg. Adeonus hints he will support the conniving governor in return for a donation to the Chapel.. but turns round and does not do so after the money is given.
Nemedia, the continuing enemy of Aquilonia, is also largely composed of Mitran worshippers. Chaplains on both sides.



B
Interpretations/Additions by players

Marriage, faithfulness, chastity
Drawing from Mitra's emphasis on honour and truth, Mitrans should stay married once wed. In the patriarchal society of Hyborian times, the male and especially the upper-class male has more leeway on this. The woman at least should stay faithful, ideally the man too but concubines and liaisons with slaves or prostitutes are not uncommon of course.

Priests, many stay chaste to devote themselves more purely to doing good works or learning or preaching.
Some female virgin or widowed priestesses declare themselves "wed to Mitra" or Vowed Virgins, essentially nun status. Can sometimes work as good protection in a hostile world.
Priests that marry are expected to remain faithful till death.

Weddings can be a purely civil affair in Aquilonia but most commonly have a blessing ceremony by a priest. [The first 2 weddings I saw ingame had a GM come as an avatar and bless the couple]

Baptism
Adult baptism, washing away sins when one has true regrets and wishes to show devotion to Mitra.

Other Ceremonies
December 21st, (winter solstice) commemorating Mitra's victory of Light over the Darkness of Set.
February 2nd, Snake smashing day. Believed that Set sends out snakes on this day in a last futile attempt to halt the return of light to the world. Get out there and kill any snake you see.
April 27 to May 3, Floralia. Marked with dancing, drinking, and flowers. Light fully in the ascendant.
June 21st, (summer solstice) Festival of the Sun. For many very joyful but also amongst the more thoughtful, time to think of how one still has much to do this year to be judged as on the side of light.
September ...21st?, Harvest Festival. Praise to Mitra that his blessings have brought another year of bounty.

Magic
The simple pure circle of protection... as opposed to the many complex shapes and symbols of the evil demons and deities of Acheron.
Clear simple words in the vernacular for the most part... as opposed to the ugly, forceful gutteral wordings of the past darknesses.

Politics
Worship of Asura is growing as a secondary deity to Mitra in Aquilonia, as Asurans aided Conan in regaining his throne recently. This fits very well with Invicta.

The hierarchy is dispersed, with no single Pope dictating for the entirety of the faithful but rather multiple centres of leadership, more akin to the earlier centuries of the Christian religion.

History
The idea that Mitra was a god, perhaps originally human that attained divinity, in Atlantis, while that civilisation still stood, opposed to the darkness that was Acheron.
This would explain the ancient and continuing hostility of Mitra and Set, as Set was a major deity worshipped by Acheronians, besides many depraved demons from beyond.

Alternatively, or additionally, Mitra was a god of the Hyborians from when they lived further east and were influenced by Vendhyan ideals and philosophies and deities. (Asura is the closest divinity in some respects to Mitra)


Some Mitran priests get very fond of their wine