Well actually, your login info never goes to them at all. You log into the sites directly in a webview and it uses the cookie to sync your subs and recommendations locally on your device.
You took the words out of my mouth. I don't even know who this guy is really, I've seen some of his videos, but having access to all of your account stuff is... nah
A 300MB apk file? It is on Google Play. No F(L)OSS license. Other apps by the same developer (futo) seem to contain no trackers. Probably nothing to worry about, but how many video platforms does the average person use? I look at YT and a small handful of peertube instances.
You are trying to download the universal app that contains multi archs libraries. Try to download a specific arch for your device like arm v7 or arm v8. That's half the size. The Play Store build is even more optimized at 41mb.
Edit: the version listed on their website has more sources compared to playstore which is bland. I would get the site version if I were you.