I doubt you'd be able to get one small enough to be portable, quiet enough for camping, and still power a heat pump or electric water heater, but a gas or oil boiler is definitely doable.  Like you're asking, we got a Yamaha EF3000iSE for multiple purposes:

1) Power my entire trailer (A/C and microwave included, but probably not at the same time).
2) Power my fridge and oil boiler at home and maybe a couple of lights.  I can get hot water from the boiler too, if necessary.
3) Power tools (e.g., air compressor and saw) when working in/on the shed at the back of my property which is ~220 feet away from the exterior outlet on the house.

It's extremely quiet, at 53dB (1/4 load) to 60dB (full load).  It wasn't cheap (the quiet ones usually aren't) and does weigh a good bit at something like 130lbs.  It requires two people or a ramp to get it in the back of the truck.  It's fairly compact and has wheels, so you can move it around horizontally pretty easy.

I have a neighbor a block over with a very noisy generator.  I can easily hear his from my house, at least 400+ feet away, and it's grating when everything else is absolutely silent in the midst of the power outage.  I swear I could still hear his over mine, but it could have been my imagination.  He ran it constantly during the last couple of power outages and I'm glad I don't live directly adjacent to him or his generator might have suffered a mysterious hyperglycemic failure during the middle of the night.  At my side property lines, about 45 feet away from where I had the generator running, you could only hear a very quiet thrum/purr from mine.