Yes. I recently disassembled an old Minoura Magturbo trainer did a bunch of tests on it. Here's a picture of the brake mechanism:

(The weird color is due to some plant lights nearby.)
Without any modification, the low frequency magnetic field strength right next to the brake was 10 to 12 microteslas (uT). Replacing the three screws on the right of the photo with non-magnetic (stainless steel) ones lowered it to 4-5 uT. Vibration makes a pretty big difference, too.
I also have a Kinetic Road Machine fluid trainer that's about 10 years old, and although it's supposed to have a magnetic coupling inside, it only generates a 5 uT magnetic field. (For that reason I'm pretty sure that it *doesn't* have a magnetic coupling. It was a production sample that I bought directly from Kinetic's North American sales director, so it's not 100% identical to a normal Road Machine.) The safest bike trainer would probably be a Cyclops from that period, since they had fluid resistance units and no magnetic couplings as far as I know. I can't help much with treadmills or elliptical machines.