I think #NotmyPope is problematic. First, he IS the Pope, whether we like it or not. Second, uneducated types may infer that you are a sedevacantist. Third, it doesn't have any information-content...while unlikely, maybe people would think you want him to go ALL-IN on female priests etc...some people seem to think he has a ways still to go.
Perhaps #RespectTradition or #StopWingingIt or even #PrayforTHISPope - something that gets across your point while still giving the respect we are supposed to render - would do a better job. Good luck.
I agree also. He is our pope and has the authority granted that position by the Holy Trinity. It is God’s will and in Him I trust. Regardless of the errors of men who are human, Christ is ever present in His church. How about #JesusisKIng #Heisthebreadoflife.