I've been using the Android Garmin Connect App, as well as the Garmin Express Windows 7 app, with several fitness trackers, without any login issues, for years.
At the same time, I also log in to the Web-site, using the Chrome Browser, version 60.0... But, when trying to do so, since recently, as long as the Garmin site shows me a Facebook Login as a larger graphical button, along with "Welcome Back, Dirk Mittler", clicking on that button simply has no effect. Yet, if I click on "Sign In As A Different User", I next get to see a variety of sign-in options, that include an email-address, as well as a the smaller Facebook Icon. If I then click on that Facebook Icon, the logon succeeds. I think this needs some ironing-out.
This same problem does not occur, when I use FireFox.
Dirk