I just used a Samsung Galaxy S8 using "Samsung Internet" v7.2.10.33 on your site. When I clicked the Login button, the popup appeared with the "Facebook" blue button. When I clicked that I was redirected to Facebook like I'd expect.
From what I can see, things are working. I have Allow Javascript and the Pop-up Blocker enabled, which seem to be the defaults. I'm unsure why it's not working for you, but I'd recommend testing different settings in the Internet app or a different browser, like Chrome, to see if that works. We'll need to understand the issue further to know where to start as this isn't something we can recreate and not an issue we've heard of before.
Thanks,
Alex