Yes. But having local polititians whine against EU regulation and then vote for it is a common pattern to get easy wins with easily led people like the original posters here.

What if politicians who voted for an EU regulation get voted out? Would politicians who opposed the regulation have no choice but to comply or leave if the majority of EU countries continued supporting it?

The newcomers will have to start a new movement and make EU change it or exit EU. EU is very bad if your country suddenly wants to be a something completely different for a few years for example, it’s much more accommodating to gradual changes over the years.

Suddenly you decide that you want to collect all the private data online and sell it to the highest bidder? Decided that cancerogenic chemicals in the food are cool? It’s not going to happen fast.

It's complex, they can be sued or funding can get cut but EU is not like the USA.

It's more like a club where the countries come together to decide how to do things and then they implement local laws to do it. They are not hostile countries brought together by force, the hostilities are usually between neighbours and EU acts as a way to resolve them. For example, countries close to the borders see large refugee influx and the countries further away don't want to have anything to do with that and EU tries to find a way to ease the pressure on the border countries(so far, not very successfully but managed to create a mechanism of keeping refugees outside of EU by paying the host countries like Turkey). Or let's say a country wants to join EU, an EU country might have long standing disputes and EU tries to find a common ground to mediate it(Bulgaria & Northern Macedonia is a vivid recent example). Or let's say there's ethnic issues causing wars and other tragedies, EU creates a law to guarantee the rights of the minorities so that the ethnic issues are no longer relevant those resolved.

If they can be sued for it, I wouldn't say it's accurate to say they can continue opposing it. Even cut funding, if they still have to contribute funds to the EU, would be coercive.

You miss the point, they can be sued after agreeing to it but not implementing it.

For example, let's say Poland agreed to GDPR but they went ahead and made itself a hub for data brokers with no respect to GDPR, then Poland gets sued and funds cut. Poland doesn't get sued or funds cut if they voted against GDPR and blocking it in first place.