Do you have the right to know certain things about your Therapist

A therapist doesn’t have to self-disclose personal things such as sexuality. It’s their business just as much as it is your business what you prefer. Therapists are taught NOT to self-disclose much boundaries are important. It may be helpful to discuss this with your t.

Buy what if you don't want to see someone with an alternate sexuality.

"Alternate"?

If you don't know about their sexuality and you have no issues in therapy with them, what does their sexuality matter to you at all?

I guess Alternate or Alternative, I use the two almost interchangeably. I guess if someone doesn't want to see someone who has one of those sexualities than they have every right not to see someone who has one of those sexualities.

Personaly I am not that opposed to it, in fact I identify as Asexual so the Therapist and I were probably as opposite as you can get.

What’s alternative or alternate sexuality? One of “those”? What do you mean by that?

Say someone who has a sexuality other than Heterosexual.