Toto Carolina Spigot to Rubber Sleeve connection.

Need to remove my 9 year old toilet to access the back of it to clean it out. Smells like a public restroom thanks to young boys using the toilet seat as a backboard. Toilet uses unifit rough in. Should I worry about the rubber seal of the unifit to the spigot of the toilet when I put the toilet back in place. Currently only have one bathroom in the house and would like to be prepared.

That rubber is pretty resilient...don't think you'll have any problems. If you haven't caulked around the base of the toilet, now you know why that is required in many places, and recommended everywhere. Use something like Polyseamseal, which can be removed a lot easier than a silicon caulk.