One of my grandfathers used to work for Nortel. One of the projects he worked on was the Trans Canada Microwave, which was a microwave relay system built in the '50s to carry television and telephone signals across Canada. The towers were installed all over Canada in remote locations and high elevations. Maintenance on the system could be required even when the weather was bad. My grandfather told me that the engineers who worked on the towers would sometimes stick their hands in front of the microwave emitters to warm them up. It's anecdotal, but I'm relatively confident that it's theoretically possible to warm people with microwaves.

Big caveat, though. Those engineers knew how powerful the emitters were, they knew that microwaves are not ionizing radiation and thus posed no cancer risk, they knew roughly what percentage of their hands was composed of water, and thus how much heat energy their hands would absorb from the emitters at a given power level. That's the only reason they were willing to do it, well that and they were probably the kind of people who got a kick out of doing something that would appear insane to most of the populace.

It seems very unlikely to me that a microwave system could be turned into a safe people-heating system for at least the following reasons:

• Feedback loops. All modern HVAC works on feedback loops. Your thermostat detects that the temperate is cold, it fires up your furnace / heat pump / electric baseboard / whatever and produces more heat. When the thermostat detects that the temperature has reached the set-point, it shuts off the heat. Current thermostats would not be able to detect the effect of microwave heating, which prevent the establishment of a feedback control loop.
• Uneven heating. Things with more water will heat up a lot faster than things with little water. This is usually fine when microwaving food since most of our food is water, in varying concentrations. If you're heating up a burger in the microwave, you can put the patty in by itself for a minute, then put the bun in for 15 seconds, then reassemble a burger that doesn't have a cold patty or a stiff overcooked bun. If you're heating up a person, you can't ask them to take out their almost-entirely-water eyeballs to ensure they don't overheat.
• Failure conditions. If your heat gets stuck in the on setting, the maximum result is probably that your house will get sweltering hot but not hot enough to kill you in a moderate timeframe. Depending on power levels, a microwave heating system could internally cook people in their sleep if it entered a failure mode where the heating got stuck in the on setting.
• Efficiency. It takes a considerable amount of power to run even a small microwave, and that's blasting microwaves into a relatively tiny cubic area. Trying to heat people would require microwaving a much larger volume, and said volume would also be moving around. Trying to emit microwaves in even a house-sized volume would probably be prohibitively costly.
• Interactions with metal and other objects. Microwaves can create intense electrical fields around metal objects, and those can become intense enough to create plasma and electrical arcs. Hell, you can create plasma in your microwave with two grapes. Blasting microwaves into a large volume with unknown contents would be a great way to create an unexpected fire.