When I'm playing Civ 5 and found a religion, I often will call it Rationality.
I often I have argued that - in Civ 5's (and Civ6's) terms, any "set of beliefs" can be seen as a "religion". It does not necessary imply a god. (as in the case of Tao).
I've founded myself "religions" as Humanism (Netherlands), Masonry (France), Ecologism (Soshone)... and so on
Fanatic sects apart, most religions only imply a set of values to direct your live, because that is what you believe it is good (in religion this tends to be because either because a supranatural entity, or the same cycle of life will reward you).
But this has no difference on having a diferent set of values because other trends that give you the feeling of being physically or morally superior (i.e., culturism, veganism), without requiring the involvement of a god. And in these cases, you can find as well its dose of fanatics that want to convince anyone of the "benefits" of its way of life, and even regect any evidence they can be doing wrong to themselves or others.
Back to topic, investing in faith in Civ5 and Civ6 is for me promoting this strong set of beliefs with wich you can convince people to join you (buying GP) or to collaborate for community improvements (faith-rushing). Does not need to be directly negative to faith and culture: as commented by others, it is enough it works as a competing yield (if you build/work holy sites for faith, you are not working universities for science). You could turn a fanatic theocracy by devoting all your resources to faith, but you can be as well a balanced state that works values (faith), knowledge (science), and lore/expression/identity (culture) in synergic ways.
Answering to the main question (how to compete vs a religious victory), it would be interesting that if you outproduce in faith the religion owner, you could challenge them for control of the religion: either creating a schism and eventually, a new religion of your own, or taking complete ownership of the religion -- and then being
you the one in route for a religious victory)