Although I sometimes have problems with Cloudflare, it does not seem to affect GitHub nor Gitlab for me, although they have other problems, which I have been able to work around.
Some things that I had found helpful when working with Gitlab is to add ".patch" on the end of commit URLs, and changing "blob" to "raw" in file URLs. (This works on GitHub as well.) It is also possible to use API, and sometimes the data can be found within the HTML the server sends to you without needing any additional requests (this seems to work on GitHub more reliably than on Gitlab though).
You could also clone the repository into your own computer in order to see the files (and then use the git command line to send any changes you make to the server), but that does not include issue tracker etc, and you might not want all of the files anyways, if the repository has a lot of files.
Some things that I had found helpful when working with Gitlab is to add ".patch" on the end of commit URLs, and changing "blob" to "raw" in file URLs. (This works on GitHub as well.) It is also possible to use API, and sometimes the data can be found within the HTML the server sends to you without needing any additional requests (this seems to work on GitHub more reliably than on Gitlab though).
You could also clone the repository into your own computer in order to see the files (and then use the git command line to send any changes you make to the server), but that does not include issue tracker etc, and you might not want all of the files anyways, if the repository has a lot of files.