It doesn't seem to be intentional. Infinity ring should either completely override the red ring, or let you shoot red rings while you have the infinity ring selected.
Current nonsensical behavior w/ infinity ring:
Infinity ring selected: Fire and fire normal both shoot infinity
Other ring selected: Fire shoots weapon ring, fire normal shoots red ring
Behavior that actually makes sense A:
Infinity ring selected: Fire and fire normal both shoot infinity
Other ring selected: Fire shoots weapon ring, fire normal shoots infinity
Behavior that actually makes sense B:
Infinity ring selected: Fire shoots infinity, fire normal shoots red ring
Other ring selected: Fire shoots weapon ring, fire normal shoots red ring
(I assume A is the intended behavior)