I find it unlikely they will be allowed to become a majority. Politicians are not dumb, they know that once they become a majority they will not need the current politicians anymore and will elect their own.
A good example is what happened in the UK. Scotland was dominated by Labour with their usual pandering to minorities, it worked very well until the Scots decided Labour was too British and against independence and voted in 2015 overwhelmingly for the SNP.
Now, the american system is different and it's harder for a third party, but I wouldn't be surprised if down the line a hispanic/mexican party comes on and takes the vote out of the democratic party.
This is hilarious considering what just happened. The threat to Western values is not coming from minorities. Trump explicitly rejected Western values and won the presidency (and minority groups were a large part of the pro-American opposition). And other politicians in the West have tried the same (Le Pen, Farage, etc.).
Fascism is very much western. It was created in Italy and refined in Germany.
Even if you talk about the USA only it was an extremely violent country founded by slave owning planters and was pretty much closed to non-white immigration until 1965, except if you consider slavery as a form of migration. Acceptance of all races and nationalities is a modern trend that might as well not last for long in the big picture.
Also you're delusional if you think these minorities care about the western values you talk about, which I assume to be liberalism. It's just that while you're a minority it's much better to live in a liberal place than an authoritarian one.
As a thought experiment, you're a muslim fanatic, do you prefer to live in Norway or China? In an authoritarian place like China it's way more likely you will get locked up or straight up disappear while in Norway you can live on government benefits, travel to Syria, kill some infidels and go back and get a slap on the wrist.
I read in another thread you talk about how most people that vote republican do so out of racism(and religiosity, gun nuttery and so on) and not because they really believe in conservatism, tax cuts, opposition to fight global warming...and I agree.
Now, 97% of black women vote for Hillary according to exit polls, do you really think that they care about LGBT rights, fighting global warming or what will happen to illegal mexicans?
Come on, you know they like the benefits.
Anyhow, the pandora box is now open, it's unlikely Le Pen or Farage will achieve much themselves because unlike Trump they don't have the backing of a big party but Farage got Brexit, Le Pen is influencing the Républicains who will probably win against the Socialists. OFP may very well win the Austrian presidency. Who knows what else will happen in 2017?