I have googled my T quite intensely when I first started to see her. I wanted to find out what her experience is, how qualified she is to work with me. I found some very insightful things and I told her at the next session that googling her made me more sure than before that she is perfect for me. She laughed about a funny thing I found online and it really was never a problem at all..

I don't google her any more now, I think what I know is enough

I want to add though, that I think it's definitely okay to google your T, what I don't think it's okay is when people use it to get closer to T by online stalking them, or sometimes intrude on their personal lives online, which I know some people have done. But googling them just to see their picture or finding out professional info is perfectly fine in my opinion.