I've worked on exactly one project where performance concerns lead to removing Fkeys.

The compromise we came to was to enforce them in dev and qa in order to catch bugs, and relax them in prod.

I still strongly believe that database constraints are a developer's best friend, in that you can trivially make your data structures fight back against misuse. This makes several classes of bugs obvious. But like anything, there are times they are not optimal.

I'll also say I think there are very few cases where a small performance advantage outweighs the costs, and would be hesitant to head down this path with a team less competent than the folks at Github.