They don't, what Transform told is you is incorrect. Obviously they both make you trip and when you trip frequently it becomes less profound regardless of what psychedelic you take, so that is one aspect of tolerance but then of course there is also pharmacological tolerance. That exists between LSD and mushrooms also but its nowhere near 100%.
Give you an example, a few years ago I was taking LSD every weekend, fairly strong doses. I was already noticing a tolerance effect one week to the next. One time I decided to take an 8th of mushrooms on thursday expecting it to be rather underwhelming due to tolerance since Id just taken a large dose of LSD 5 days before that. Let me tell you, those mushrooms rocked my world. Granted they were penis envy and extremely potent but I still remember that trip to this day. It was one of the most unforgettable trips of my life and put the fairly decent acid I was doing to shame.
So yeah, cross tolerance definitely isn't 100%.