Is this center support bad?
 

I've been chasing a possible driveline noise and slight vibration. I know I need a rear diff output seal, but is my center support/bearing bad (pic attached)? There's no noise if I rotate it slowly, and the front looks normal. The rear rubber seems detached from the collar. There's the metal collar of the mount, then a non-metallic ring, and then the rubber. If I loosen the mount, I can get the rubber to slip past the non-metal ring, and I can put a screwdriver in there. Is it supposed to connect or is this normal? I can push the shaft laterally over 1/8", but not a huge amount.

I've seen threads saying the center support needs to be pressed on. Is this so, or is there a home version of the procedure?
Thanks!

that looks dried, if it was never replaced, it's about time. you need a 3 prong puller to pull it out, but don't need anything to press it in. The new support bearing comes with the whole bracket.

If that's the center bearing for the driveshaft, then get a new one before it leaves you stranded. They're not that expensive and only and hour or two to replace with hand tools. I did not need a puller, but mine failed at 80 mph and DID leave my wife stranded--300 miles from home!