Most rubber dishes can go in the dishwasher and come out just fine without melting or anything bad like that.
However when you do put rubber in the dishwasher the dishwasher detergent can sometimes overtime dull the rubber and degrade the rubber.
So if you do wash rubber dishes in the dishwasher it can eventually degrade the rubber dishes and make them nearly useless.
I would recommend just hand washing the rubber dishes but if you want to wash the rubber dishes in the dishwasher you can do so.
But just be aware that the rubber will start to eventually dull and degrade but it will usually take several washes in the dishwasher for that to happen.