At a theoretical level, religion is the sum of the spheres it governs (simply put), nothing more. To get empowered, is to grasp a single part of the religion, to get a tattoo is to fully embrace it as a whole.

But, at a more practical level, many IMMs also represent certain ideologies. They lead certain Cabals, which have specific ideas about the way the world should work.

As a Priest, you may wish to embrace the Religion, but not the Ideology. For instance, you may be inspired by Thror's religion, while not wanting to forego the use of magical items.

My question is, how limiting is it, to follow a religion, but not the ideology.

In general, not very limiting. You can find plenty of past examples of priests/tattooees who are mage followers of Battle gods, Outlander followers of Empire gods, and so on and so forth.

That being said, there's obviously some degree of overlap between the two. For example, Yean's religion doesn't mesh well with some kinds of mages even still.