Multiple grounds from diode bridge? Safe or really stupid/dangerous?

Yes, you can do that, even need to do that if each of the AC feeds in your schematic come from separate transformer windings. Put another way, the two AC feeds must be floating with respect to each other.

With the AC feeds floating, the DC voltages derived from them will also float. If you want the circuitry powered by one to drive a signal to the other, you also need to connect one other point between the two sections that will be the reference voltage for this signal. The negative of the DC supply is a obvious choice, and it simplifies thinking about the circuit if you consider that to be the ground for both sections.

Assuming you aren't regarding the whole circuit as potentially at mains voltage wrt ground and appropriately protected, then you need two isolating transformers, as noted.

This reminds me of old valve televisions which often had a hot chassis. They were (very nominally) safe because the entire system (including the speakers) was inside an insulated enclosure (having said that, there were numerous accidents where somebody managed to contact the chassis regardless). I doubt they'd be to code today.