Would they though? From what I understood Google has a workplace that heavily leans towards one political side in the US. It seems to even have been used to shame people to stay in line. What's the chance that something similar wouldn't happen with this Union?

There are no "closed shops" any more in the UK[1]. Any member can leave a union any time they like.

[1] https://en.wikipedia.org/wiki/Employment_Act_1990

Even voicing the opinion that Right to Work is a good idea causes the pro-union folks to act like they're going rabid, acting like you're trying to tear down their entire world. Passing a Right to Work law is, in the eyes of many, a flat out attack on unions and an act of union busting.

Rendering the contracts that unions sign with employers unenforceable is pretty much the definition of union busting.

It's explicitly about preventing two consenting parties (union + employer) from freely entering into a contract.

Oddly enough there are some (libertarians) people who consider the right to enter into a contract freely pretty sacrosanct, but I've yet to hear one complain about this law.

And that will stop people from shaming you on social media how? All you need to harm someone is to send a Twitter mob at them. If your union becomes political enough then toy can just do that, just like Google did.

In political terms most Google employees are centrists, wet one nation troy or Eisenhower era Republicans.

And Prospect is explicitly not "Political" with the Big P i.e. aligned with a particular party - in fact almost all Professional unions are as they have members of all political parties