Yes. I was going to post what Smileygal posted already. Fully in agreement with that post.

What I'm trying to add to it is just that deep therapy is going to be very personal and will involve attachment and lots of trust. It's one reason why I chose not to enter it again. I can't and won't put in effort for managing a personal attachment in therapy. If you feel up to it, feel free to, if not, then that's okay too. My point is, make an informed decision on whether you are going to be able to trust enough and put in the effort like that. I personally chose alternative routes, such as, a LOT of psychoeducation on my own, a LOT of journalling, reflection, talking in support groups, talking with other mental health workers (not therapists), talking to some people one on one with similar issues, carefully - sometimes chaotically - finding support in family as well. Frankly I find those one on one talks only worked if someone was either having VERY similar issues to mine, OR very emotionally intelligent, in a good mood to be able to take on the talk with me, generally caring about people and keeping good boundaries scheduling talks not too frequently and not too long each time.

One more comment. Your feelings are by definition valid. The question is, what will you do with the feelings, as far as interpretation, taking a perspective for them, and whether you make decisions & act on them and how. So you can accept these feelings and then you can see where they come from if you think that would be insightful for you, or you can simplify and skip that part and instead just discuss with the therapist, that you don't want too much disclosure from them, or if they want to illustrate things with examples, then use less personal ones. Etc etc, these are just two possible options

I hope some of that input helped.

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EDIT: I wanted to add more.

The questions about your being gay, it sounded like, she doesn't know a whole lot about gay people. It sounds like most people who don't know a whole lot. Not malicious or manipulative or any hidden motives, just that. I have a gay family member. But a lot of people in my country are not at all educated on the topic. I imagine not everyone in the USA is either.

If it is important to you that the therapist understands this topic well, then you do need to find someone else.

My family member btw only realised i.e admitted it to himself when he was already in his twenties - due to religion issues. He obviously knew something was up before it too but he tried to deny it hard and even tried to date a girl and so on. So I wouldn't get too hung up on word usage. But if the topic is sensitive then it's understandable you would be bothered and uncomfortable. This is why I said maybe find another therapist if this is going to be an important/often mentioned topic in therapy.

I agree with the post too where it's mentioned discussions about countertransference really belong to supervisory sessions. Sounds like she got too enthusiastic about giving you education about how the therapy process works

You asked if it would make anyone else uncomfortable. As far as myself, it depends on how it was delivered - if there was lots of details indulged then she still needs to work on some of her boundaries and I'd let her know I'm not comfortable and not okay with her disclosing. If details were not indulged at length, then I'd be comfortable okay. As in, I'd probably not be very interested at all in that part or I'd try to focus on the education she's trying to give to me about it.

Also, countertransference is basically a fancy term for, the therapist is human too and is going to have various feelings and reactions about you. I'm not really worried about what we call it, but this phenomenon does exist and it does have an important role and it has to be managed and all that if the therapy goes deep enough.