I think you are allowed to feel what you want about it. It really sounds like it's not so much about the change, but more about feeling secure and needing consistency. If you're open to seeing things differently, maybe cancelling but still making sure you're needs are addressed by offering another appt in the same week could be considered consistency?
My T is going through some things, and has done several changes over the last few months. She always makes time to see me within a day or two. That, to me, is a sign of caring and respect for our therapy that I sincerely appreciate. I understand things happen, and respect her need to take care of herself. Otherwise she might not be able to be there for me.