I'd distinguish between existentialism as a genre, niche, and method, on the one hand, with the doctrines that particular existentialists propose, on the other. Existentialism in the former sense merges even with something like Kantian transcendentalism. It's just a question of figuring out the most universal, fundamental aspects of life, the ones that make up our existential condition, and determining how they impact us on a daily basis.

There are religious and atheistic existentialists. But even the reigious ones are less theological or dogmatic than non-existential theists.

There's a fine line here in saying that the existential discouse should replace the spiritual one since I'm not saying that everything existentialists have said should be accepted. The writing style of some leading existentialists, for example, is pretentious and overly complicated. What we should search for, though, is a fresh philosophical vocabulary. The spiritual one is quite stale, and science has made it obsolete.