non-ionizing radiation, which does not damage cells or DNA

well, that's the point of the discussion because there is not consensus that is true:

"When theory and observation collide: Can non-ionizing radiation cause cancer?"

https://www.sciencedirect.com/science/article/abs/pii/S0269749116309526

Evidence of free-radical damage has been repeatedly documented among humans, animals, plants and microorganisms for both extremely low frequency (ELF) electromagnetic fields (EMF) and for radio frequency (RF) radiation, neither of which is ionizing. While IR directly damages DNA, NIR interferes with the oxidative repair mechanisms resulting in oxidative stress, damage to cellular components including DNA, and damage to cellular processes leading to cancer. Furthermore, free-radical damage explains the increased cancer risks associated with mobile phone use, occupational exposure to NIR (ELF EMF and RFR), and residential exposure to power lines and RF transmitters including mobile phones, cell phone base stations, broadcast antennas, and radar installations.

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Microwave ovens do not expose tissues to microwaves

I guess there would be concern that they could if they leaked (microwave harm reduction as a related topic)

Microwaving food does not affect its nutritional value negatively

I think it's accepted that it does, along with cooking, but this was thought to be a trade off for killing possible diseases.

can preserve some nutrients better than other cooking methods, such as boiling or frying, because it reduces the exposure to heat and water

That would be true all else equal, but it's argued microwaves possibly create unique damage

This is not unique to microwaving

Raw food advocates would argue against microwaves and other non-microwave cooking methods though

The Swiss Federal Office of Public Health, which issued a press release in 1992 stating that Hertel’s study was not scientifically valid and that there was no evidence that microwaved food was harmful to health

it's possible they could be correct but also possible this is a fallacy of appealing to authority