Are mushy plums OK to use in cooking? I have some plums that have started to go soft and squishy. Would they be OK in crumble / crisp / cobbler type recipes?

(I can't taste them before cooking because I am allergic to raw fruit).
As long as they aren't spoiled they'll be fine for a crumble/crisp/cobbler. You'll want to have someone else taste them to make sure first. They may need less sugar and less or no precooking. If they are really, really mushy then you might want to add some firmer plums or other fruit to give some texture.