I own and manage about 100 student rental units. Lots of toilets. We had a toilet mystery once. Toilet would clog with any solid material but would pass water well when flushed with only liquid. Snaked it many times. No joy. We finally pulled the dang thing, put on the long gloves and explored. Pulled out lots of Q-tips. The tenant threw them in the toilet each day and they caught just right in the trap. The snake would punch right through them, water would flow right through, but solids got stopped.
I've pulled lots of things out of toilets. If it isn't mineral deposits, it's a foreign object. Just pull it and you'll find your problem.