What an irony, Twitter is available on Tor, but it won't let you browse for longer than 0.3s without forcing to log in.
Sort of unrelated, but you can bypass the login prompt if you click "login" and then click the X in the upper left of the popover.
twitter.com##+js(cookie-remover, guest_id)
in ublock origin as a rule works reasonably well to remove the nag screens.