Seems to happen with some china, in my case old big china dishes with a “microwave safe” note under them did work as advertised, but after 4 years the dishes now heat up with the food too.
It is not an issue with the microwave oven because it happens in 2 different microwaves and a new set of dishes does not heat up.
The glaze coating the ceramics become crazed (suffused with microscopic cracks) over time, allowing things to get trapped in the surface. I don’t know specifically which substance causes the heating, but it could be water or substances dissolved in the water. Try soaking an older mug in vinegar overnight to dissolve out anything trapped in there, then dry it out in a 200-degree oven for a couple hours. I’ve never tried this myself, but I’m told it often works.
Almost any dish will heat up with food in the microwave, even brand new ones. For some reason there is a common misconception out there that microwaves don’t generate ‘real’ heat in some way. This extends to a belief that microwaves can’t start fires and won’t heat dishes. None of this is true. Dishes labelled microwave safe only conform to two standards: they won’t shatter when they are heated and they don’t emit toxic fumes when heated. That’s it. Microwave safe dishes can and do still get hot. They can and do melt. They can and do crack, dicolour and are otherwise destroyed by normal use.
As for why your dishes are heating up, it could be any number of reasons. They could have absorbed water or fat as you suggest, or the glazing could have crazed and the smaller peices become less capable of dispersing heat. It’s even possible that the ceramic has been chemically altered by years of constant baking.
I’m assuming that you have tried to cook exactly the same food in exactly the same oven to confirm that it is the dish that has changed?
Anyway, as far as the actual question asked, the answer is “no”. Your dish is just as safe today as it was the day you bought it. It still won’t shatter and it still won’t emit any toxic fumes. Since that is all that “microwave safe” means your dish is still perfectly safe. The fact that it now warms up doesn’t make it any less safe for use in a microwave oven.
Yes, and I do know dishes usually do heat up a little and one can handle them with no problem after cooking, but these ones (The china is yellow in color) do burn your fingers now after a minute in the microwave. They did not do that before, and indeed with the same food the new china (white) does not have that issue.