Related, but no longer reproducible: Link not working in profile description
I created a new account for my bot on Stack Overflow, when I noticed that none of the links in the "about me" section and also the link to a custom page (the one with the chain icon on the right side) worked.
I guessed that this was due to the new users limitations, which are removed after you reach 10 rep.
[New users can't] post more than eight hyperlinks at a time, either in a post or their user profile.
How it looks, this has been reduced or completely disabled in the meantime. Anyway, the FAQ on meta.SE, SO and very likely all other sites should be updated to state correct information.
EDIT: Please note that the question isn't about the network profile page, I understand that links are disabled there (See the comments). The problem relies in the FAQ/the site-specific profile. The reason posting that here and not on meta.SO is that this problem likely relies also on other sites.