Hi Robin,
I’ve checked MarketPress, and it doesn’t directly hook into bbPress anywhere. Instead it only hooks the standard WordPress profile.
It looks like bbPress just piggyback’s off that action, (see bbPress functions.php line 959) which is why those fields are showing up.
Doing something like this should remove it.
global $mp;
remove_action('show_user_profile',array($mp,'user_profile_fields'));
remove_action('edit_user_profile',array($mp,'user_profile_fields'));