I'm more curious as to why or how this impacts on you. I understand the need to be similar to the therapist in your beliefs and values, but beyond that, with time and especially if you look up her personal or other professional pages online, you're bound to find differences. It could be a hobby, it could be something she personally believes in and wants to offer to people who also believe in it. As long as she doesn't try to push it on you (which definitely should not happen), I wonder if maybe this focus on what her views are might say something about personal fears and a need for structure and predictability.

Most importantly, how is your therapy with her going? Do you have a good therapeutic relationship in which you feel you can trust and open up? Do you notice progress? Is her approach with you (not what she may write online) what you need? In the end, I think these are the most important aspects to consider.

In my experience when something like this seems so upsetting or frightening or offensive, it means an important issue or dynamic has been touched. IF she can keep a professional attitude with you, I would suggest trying to work it out and see if something valuable to you can come out of this.