When I try to do that from Tails OS, it tells me that the website is trying to extract HTML5 canvas data that can uniquely identify my computer.
How do I get around this without violating my security?
Upload your profile photo to a photo sharing web application such as Imgur, and point your Twitter profile to the profile photo that you uploaded. Images uploaded to Imgur are anonymous. They cannot be searched and only those people with whom you share the URL (or your public images URL) will be able to see it. Due to privacy concerns, EXIF data or metadata is removed on upload. There is no setting available to retain the data.