I am one of those that believe there is nothing wrong with looking up public info on anyone on the internet, especially not our therapist that we share so many personal things with but they don't reciprocate (or not to the same extent). But I am beginning to think perhaps I am in the minority thinking this way as similar issues come up here on PC very frequently, people feeling torn or ashamed about googling the T. I tend to really believe though that it is not the privately looking at public info that is intrusive, but questioning the person about things they don't mean to share with us.

Maybe one thing to consider, other than it may be a mistake / automatic follows on his end, is (as mentioned by others as well) that many people do not believe there is anything wrong with adult porn, if it is kept in its own place and is not abusive. It does make sense for a T to be sensitive to this and be aware than many clients may have strong negative feelings about it due to their own histories or different morals, but they might just want be free in their personal lives. If they do want to make those connections related to sex, they would probably not get as many with a private account. I do very much think it is not good for the professional image of a therapist (or anyone in responsible, visible positions) to be so transparent about stuff like that, but some people just don't want to mask their whole life for that reason.

I personally would be careful about questioning the T about this and would think what I would want to get out of such a discussion. What could possibly happen and would those outcomes feel satisfying? For example, the T might immediately recognize that you felt disturbed by this and just lie, say that those were just automatic follows and maybe that he wasn't even aware. You could never know the truth. Or (more likely) would want to investigate with you why it bothers you - would you find this useful? Is it related to what you are in therapy for or things you feel uncomfortable and want to change in your life? If yes, I would also suggest to tell him but if not, what would be the point? Maybe to ease your mind sharing your feelings, that could also be a good reason.

If the T is using his Twitter for professional purposes (as many people do), making it private may not serve that well.