JBL called that surround material Lansalloy, and it was supposed to last forever. It does last a long time, but it hardens over time. It's tricky and tedious to peel it off. You will be amazed at how much better they sound with proper new surrounds. I always cut the cap and shim the VC, but I also have new dustcaps and proper black lacquer based adhesive. Speaker Exchange (no affiliation) sells the Moyen 3087 adhesive in small tubes and a refoam kit with new dustcaps. The dust caps they have are a bit big, a purist might complain if they notice.
If the caps are electrolytic, then yes, replace them. If mylar or oil, leave them be.