I just want to say a couple of things: it's absolutely possible to be both religious and scientific. I don't understand why people often oppose the two. For instance, the guy who discovered the Big Bang was a Jesuit.
Just so we're clear: I'm a hardcore atheist so I am not talking about myself but I know two
scientists who are also Catholic. Catholicism as a whole is perfectly cool with science.
Also homeopathy is not totally bogus: it's based on plants, sure the effect may be limited but it sometimes works. The placebo effect is also a thing that exists.

So far your therapist doesn't sound like a quack.
I would be more concerned about the center she works for as a counselor. Could you ask her about it? Personally woo-woo nonsense would be a dealbreaker for me.
I understand your reticence about her possibly using one of those techniques in your therapy.
All that said, I agree with stopdog: psychology isn't a science. It's an art (as my ex T used to say).