If they'd offer me FREE FOR A LIMITED TIME NOW I'd pass.
If they'd say it's part of an experiment, maybe. But that would ruin the experiment.
Plenty of cities have free newspapers given away at train stations and suchlike [1] - they're packed with adverts and owned by sketchy billionaires, of course, but so are most newspapers you pay for.
Being "the product" is only horrible if you're being infringed upon (tracked, for example) in the process.
I am reminded of watching Geritol ads as a youth. That was the price of enjoying The Lawrence Welk show. Saturday cartoons were paid for by Tony the Tiger.
TV commercials were broadcast at a significantly higher volume than the content they were embedded into. They knew you were leaving the room during the commercial breaks.
I think that most people don't mind that level of targeting or the printed ads in a newspaper. I agree with you that it becomes intolerable when the advertiser gets to know if you personally are leaving the room to run to the fridge or to run to the bathroom.
But at least you can foil a lot of that by putting your phone into airplane mode before getting anywhere near the store, paying in cash, and not using "loyalty" cards.