What could cause my toilets to bubble and clear water to come out of the clean out pipe?
This sounds like your leach field is possibly blocked. That's the disaster scenario where you not only need the tank pumped, but the yard dug up and a new field placed.

Water from your laundry coming up in your tub is a sign that it's not draining to the septic system. This is either because there is a block in the system before the tank or because the tank is unable to accept any more water as it is plugged on the discharge / leach field side.


  When I opened up the clean out pipe clear water came out (about ten gallons). I shoved the hose down about 25 feet and it was running full force but it seemed like all the water coming out of the hose was draining back out of the clean out pipe.


... and that's the sign that it's doing option #2: the tank is full and failing to drain.