On Pets I am currently seeing a mix of English and Portuguese badges on my profile:
This is true on the badges pages too -- the one listing all my badges, and the badge-specific pages that show all users who have the badge.
I do not see this for the same badges on other sites (I checked Yearling on MSE just now). I checked some other users with one of these badges on Pets and others show the language change too; it appears to be something about specific badges on this specific site.
I'm aware of this question about Portuguese notifications (also from Pets). It was reported to be fixed. Looks like either it broke again or the notifications fix needs to be applied elsewhere on the site too. (I note that it was reported as fixed in July, and I think I would have noticed this before if it'd been like this all along.)