'Cuz nothing will hurt the porcelain, it's the toilet and pump and hoses that can be damaged by household chemical cleaners...and that includes household bowl chemical cleaners that you squirt up under the rim at home. You can't do that in any marine toilet...but you CAN put on some rubber gloves and squirt some onto a sponge or wet paper towel and use that instead of a bowl brush...then wipe it all out.
Before we came up with C.P. (part of the product line I sold to Raritan 12 years ago), I'd put a little Comet on a sponge to wipe out the bowl...wiping up most of the Comet before flushing the toilet to rinse.
Since you've set it up to use sea water, I'd also recommend that keep a good supply of distilled white vinegar aboard...a cupful (any more is wasted) down the toilet once a week will prevent sea water mineral buildup. Don't leave it sitting in the bowl...flush it ALL the way through to both the thru-hull and to the tank.
If you didn't do so when you installed it, I suggest you tee a line off your head intake into the head sink drain line...that'll give you a safe way to flush clean fresh water--and vinegar--through the WHOLE system to rinse it out. Anything poured into the toilet only goes out the discharge...it doesn't make it into the intake. We can discuss details of how to do that without undoing what you've done if you want to contact me directly.