The simplest way is to disable animated avatars for all users, which certainly is not a popular measure, but as it usually happens in today's world, the majority mostly pay for unreasonable actions of few people.
True. Given that this has already been done, but not applied retroactively, as the various bounty campaigns come to an end then animated avatars will slowly disappear, save for the few users with animated personal avatars. The latter group are almost always very subtly animated and not nearly as annoying as having the stake.com visible 5 times per page.
In the meantime, if anyone is fed up with the animated bounty avatars, then see this thread for instructions on how to disable them locally:
Stop animated images in FireFox / Tor browser / Chrome.