Stereo on 1988 RX7 GXL
 

So, while the radio works fine in my RX7 the cassette player is just annoying. As, it will jump between play/pro and only play the music when it is on play. Although, I have tried using a cassette deck cleaner it still continues to have really muffled sound if it chooses to play. However, the radio works and has super nice sound, so do I just have to replace the radio or is there a fix to this? If I do have to replace it does anyone have any recommendations?

Just forget you have a cassette player! I also have an 88 also and the tapes are now 34 years old and I find the iron oxide coming off. I even ordered NOS blank cassettes and the same thing happened they are all deteriorating like color photos from the 50's.
Just enjoy the radio, it is a nice sounding system as is. Here is a tech thing, the am band uses the antenna built into the windshield, it plugs into the radio underneath the windshield grill. It also uses a ground through the firewall which has a spade connector on the engine side which has a ground wire running to a bolt on the transmission housing! I always wondered what that was for.
When I purchased the car new, I noticed ground straps from the floor pan to the mufflers, of course they were removed with the first $400 muffler change at the dealership. The ground straps are to stop the static electricity that builds up as the exhaust flows through the mufflers and interferes with the radio. So if you want the best sound you will need to ground those mufflers!

Most likely the rubber bands inside the player are shot- probably stretched out. I have an 1988 convertible and the cassette did not work. I opened the cassette player and replaced all the rubber bands (which were stretched and hard) and it worked great after that. you can buy packages of rubber bands online that should have the sizes you need.