Bandsintown automatically tracks artists you like on Facebook if you login with Facebook or if you choose to connect to Facebook during onboarding. If you do not do either of these you can still connect to your Facebook later through Settings and scan your likes to track them.
On iOS:
Tap the Profile page (person icon) at the bottom right
Tap on the Settings button (gear icon) at the top right
Scroll to Facebook
Tap Connect or Scan
On Android:
Tap the Profile page (person icon) at the bottom right
Tap on the Settings button (gear icon) at the top right
Tap Facebook
Tap Connect with Facebook