What’s being discussed by Harris/Biden is the upper tax margin for long term capital gains. If you sell a house and then buy a house, no long term capital gain there to be taxed.
But even if you just sell your house and want to go on renting for whatever reason not all of it will be taxed with that margin. Those margins apply to the amount of money that is over the cap for that margin.
For simplicity let’s say there are two tax margins, 20% for capital gains below 400k and 40% above that. Then you gain 600k by selling your home. Your tax will be calculated like this:
400k * 0.2 + 200k * 0.4
So yes this might affect some house sales but depending on where that 44% margin will be applied it’s only going to affect a very little percentage and likely none of the “low to middle class” house owners especially not if they sell property to immediately buy new property.