FB login needs refresh to work.
For FB login to work, the page needs to be refreshed manually to show logged in.
I found a previous answer to this question regarding the issue stemming from a caching plugin. It helped me figure out it was due to caching plugin: https://wpdiscuz.com/community/bug-reports/facebook-login-needs-page-refresh-reload-to-work/#post-6106
I use W3 Total Cache along with Cloudflare. I DO NOT minify JS in W3, but do in Cloudflare. When I deactivate W3 the login works as it should. When W3 is active, it does not work. so it seems to be an issue with W3 and not Cloudflare. Since the only place in the plugin to exclude js files is in the minify settings (the only place I can find), I am curious as to what else within the plugin could be contributing.
Try to exclude the files from the "Never cache the following pages" section. Helpful article: https://www.redbridgenet.com/how-to-exclude-specific-pages-from-w3-total-cache/
It appears to be the Browser Cache section that is causing it.