1. Do you have site_url *context* settings for the other context(s)?
2. Is your base href tag uncached?
<base href="[[!++site_url]]" />
3. Are you using the &contexts property in the Login tag?
[[Login? &contexts=`web,othercontext`]]
TBH, I've never used Babel so I'm not sure what else to try.
One more diagnostic thing would be to put that IsLoggedIn snippet tag on the Login page and redirect to the Login page. If the use is shown as logged in, it suggests that you're forwarding the user to another context that the user is not logged in to.