When you're ~stalking~ visiting a random github profile and happen to see that they have a <username>.github.io repository, there is no quick way to visit that homepage. Your only options are
Some sort of a quick "Go" button next to the repository name (both on the repository listing, and when you open the repository) which takes you to the webpage.
Maybe add it next to the Users profile photo if we detect that the user has a github.io page.
It's already available as a feature on GitHub, if the user opts-in to let it be on their profile. The same goes for repository view.

Also some people have a custom domain name connected to their user.github.io domain, which again, is a duplicate thing to be handled.
Hi,
I agree, this was in the case that the user chooses to put it up as a part of their profile.
In the repository view, the user can again choose to put it in the repo description or the README, however may not end up putting it.
In both of these cases, the github.io is either lost or becomes a little more painful to visit. I still believe that there is a case to be made for this feature, but I might be wrong.
It would kind of make sense, but @notlmn has a point: if the user wants that page to be visited, it should be set as their URL or mentioned in the user鈥檚 README which is now so prominently displayed.
Just want to mention that you can also drag the repository name (example.github.io) to browser's tab bar to quickly open it. I use this trick myself.
Regarding the feature, it may not be qualified to go into Refined GitHub, in which case I can write a user script for it (if I find the time).
Yeah actually my comment only applied to the User鈥檚 profile, but both other locations make sense.
Just want to mention that you can also drag the repository name (
example.github.io) to browser's tab bar to quickly open it. I use this trick myself.
@kidonng oh this is really smart, will use this.
@fregante Can I work on this?
Yes please! This can be a single feature with two init functions: one for lists and the other one for the repo root.
On the list we can use https://primer.style/octicons/link-external-16
On the repo root, look for a link in the sidebar, and if it doesn鈥檛 exist, replicate it exactly with the same DOM.