If I’m not allowed to sit outside a pub and drink alchohol becuase it might offend muslims who might see me (it has happened) is that not a removal of part of my cultural identify based on an (and to quote cougar) invasive culture which is not my own?
Well yes, but that was one person’s poor decision, not a cultural shift. There are more beer gardens now than ever before I’d guess.
Back to the OP – it’s specific beliefs that are left or right wing in flavour, although it’s far more accurate to use the two-axis model above. So people themselves can have different ideas on how to solve problems of government.
The issue is that we have political parties. So a party is aligned broadly on left or right terms, but within that party there will be loads of variation on both axes of that graph. That’s why they bicker amongst themselves. You don’t have to subscribe to current Tory party ideas to be a Tory, or even to be a right-winger.
Certain ideas do have a lot of concurrency though. Libertarianism is quite closely linked to free-market ideology I tihnk, so those things both tend to crop up on the right.
In reality all four poles have their problems, and they are probably best solved by taking ideas to a greater or lesser extent from their opposite points.
Which is why we’ve arrived at a generally centrist position as a nation, and we’re not communists or the Wild West.