I would say depends on the person. because somethings may be personal to you but may not seem like it to the therapist.. some therapist are so used to hearing personal things. its should not bother a therapist to hear such things.. but telling them might feel uncomfortable to you..
I try to find common grounds when something personal is asked I let my therapist know that it was to personal.. if she would continue after we discussed it bothered me I would find another therapist because she is not respecting my boundries I have set for myself.. just as they expect for you to respect there boundries... I believe therapy is a professional relationship between the therapist and client and these type of things are how we figure things out about ourselves, and the therapist can figure you out and help you more... more on the reason.. as why did that bother you??