As a (I hope not shitty) cis dude, I don't think I would get "furious". Id probably laugh honestly. I get where this meme comes from but it gets a bit depressing when people get put into groups and defined by things such as being cis. I'm cis and I can't change who I am, I know that there are many cis assholes but that doesn't make me one. I hope that one day these types of stereotypes disappear and we can learn to finally get along. One day...
If you wouldn't dress up as a girl to be funny because the joke is trans people, you're not a shitty cis. You can still dress up as a girl though, and you can absolutely do drag. Nobody is gatekeeping this. Stop apologizing.