is it possible this might even end up unifying domestic polarisation in western politics, except for extreme left.
You would think and hope that is a natural outcome and that is what will happen in a couple of countries but
tbh, most of these countries are on an irreversible slide. The population feels no deep attachment to their culture, certainly not to their religion and such people lack the motivation to fight back hard. Most have given up on their countries even though they see what is happening. Most seem resigned to the fate, only consoling themselves that they won't be around to face the inevitable even if it means abandoning their progeny to an uncertain fate.
"..
For the ashes of his fathers,
And the temples of his Gods..."
Unfortunately the above no longer applies. The people have been conditioned to no longer publicly feel pride in their culture and history, scared of being labeled racists...add the charge of Islamophobia and they are pretty much a beaten bunch. A stupid educational system producing too many morons in the sociological field and they are all out marching for their own demise. The tragi-comic situation of the LGBTQ community supporting the Muslim rallies (as was the case in India) shows their suicidal path.
There will be outlier incidents of fighting back like Brexit & Trump winning but that is a rank and file revolt with their desperate last hurrahs. The leadership on the right is super thin and heavily discredited. A sustained fight is necessary and the time frame for that fight is narrowing. I'm pessimistic even if I really would be happy to be wrong on this one.
The parallels with India are striking. Leftist parties opening up for mass migration because they think the immigrants will vote for them. Muslim migrants are more preferable because their religious beliefs will clash with centre-right and conservative parties and therefore are not at risk of changing preferences. We are seeing the natural outcome of that now. The tail is firmly wagging the dog.