Should gable louvers be used on the same roof that already has another type of exhaust vent?

Never mix any two types of attic exhaust vents on the same roof above a shared attic space. That includes gable louvers.

No. Gable louvers are a type of exhaust vent and should not be mixed with another type of exhaust vent on the same roof. However, many homeowners like the aesthetic touch gable louvers add to the house and would rather they remain in place even if another type of exhaust vent were installed on the roof. A quick solution is to block off the opening to the gable louver from inside the attic with plywood, Styrofoam or plastic sheeting. Blocking off the opening successfully prevents short-circuiting problems, maintains the aesthetic appearance the homeowners prefer and avoids the hassle of re-siding the house.