I think most companies will comply. A lot of them already are. In fact, I think it will be a welcome relief to them.
Back when the whole nation was captured - police cars painted, trains painted, road crossings coloured, every shop from decorated, lesbians kicked out of pride, governments saying that women had penises, the prime minister saying that 'only women have a cervix' is wrong and should not be said...
Everyone had to go along with it or be branded hateful, transphobic, bigot, terf, etc. They went after businesses. Advertisers had to toe the line. So did publishers and the media. Everything, it was absolutely everyone.
There was no choice. Businesses simply could not afford to not join in. It wasn't enough to sit back, they had to pay Stonewall to be on the 'good' list and they had to virtue signal to show the world and keep themselves safe. They were terrified. It was very much a 'do it to Julia' situation.
So now, the highest court in the land says that has to stop. It's out of their hands. They have no choice. They must comply with the law. And I think they will.
The rest will slowly get sued.