Well i tried to upload avatar and also header on twitter with Tor Browser and it's not working. I have tried with and without NoScript and different configurations of browser - nothing is working. I don't have any message from Tor Browser, just a message from Twitter saying: "Your banner failed to update because some media didn’t upload."/"Your avatar failed to update because some media didn’t upload." There's also no "Allow in future" option or just ANY option. Is there any way to deal with that?
I've confirmed this with my own twitter account. I do not see the same issue with other browsers with Tor. The only thing you can do is use a different browser.
Note: Generally speaking it is poor practice to use other browsers than Tor Browser because you can my more easily fingerprinted though you are still anonymous. By logging into a Twitter account, you are fingerprinting yourself therefore this concern is pretty much moot when using Twitter. Twitter still won't know who you are unless you dox yourself.