Really doubt even phones are dosing us the way nature does.

Having a full strength cell tower transmitter inside your home is not safe due to the intensity of the transmission, it will directly heat tissue inside your body.

Would it heat tissue anymore than the Sun (in warm places) or your heater or air-conditioner set to heat already does 10x stronger?

If you were to step into the beam carried by a waveguide for something like a powerful TV transmitter, it will cook you through like a death ray out of science fiction. Fortunately it's not actually collimated, so just a few feet away the energy is barely enough to cook your retinas faster than your blood supply can cool them (which can cause blindness). Otherwise, yes, it's much like infrared heating effects. If infrared penetrated a few centimetres deep, anyway.

While fob frequency is microwave, isn't it also much lower energy compared to, say a microwave oven, powered by mains power to cook food?

And also the fob operating in the low 100s of Mhz, not GHz, wouldn't that make it less dangerous?

^ this guy literally does nothing more than lay a long wire out on the grass, and touching it instantly smokes and burns his skin