There are six gods in the Fractured universe.
There are limitations to what gods you can pledge to, but not as strict as you may think. They don't depend on your race directly, but on your alignment. Some matches are obviously impossible, like a Beastman pledging to Babilis - unless the Beastman decides to betray its own race and turn to an Evil alignment. Neutral Gods don't care about your Karma.
You'll be able to devote yourself to a god for various blessings, and Divine schools of magic. You can only worship one god at a time.
Elysium, the source of Arboreus’ primal energy
Tyros, God of light and justice
Nelena, Goddess of the wild and mother of all beastmen.
Iridia, Goddess of fortune and mother of all humans
Galvanos, God of knowledge and keeper of the nine paths of magic
Babilis "...twisted and dark God"
A Temple Offering is a monetary donation that can be performed once a day in the home of one of the Gods of Fractured.
Temple offerings are an effective – albeit expensive – way to change your Karma towards that of the God you’re donating to. Offerings given to Elysium, Tyros and Nelena have a positive effect on your Karma, while money pledged to the dreadful Babilis cause a heavy Karma loss. Donations to Neutral Gods such as Iridia and Galvanos instead have no impact on your moral stance.
Other than (possibly) changing your Karma, a Temple Offering increases the favor of the God towards you. If high enough, you might even get bestowed a Divine Blessing, or assigned a Divine Quest to carry out!