Why isn't it simple?

>but that strategy has been tried many times before and it always ends in violence

Then don't import people of divergent/adversarial cultures who aren't willing to integrate into your country and are only there to extract the monetary benefits of your society without conforming to the laws, customs, social contracts, cultures and obligations that society requires.

If you only accept people who gladly accept your culture and values, there is no violence. History has proven this yet it seems like uncharted territory to some people. "you mean putting the fox in the hen house ends in violence?!"

>First off, who is "our"? Is it the majority?

It's the amalgamation of culture, history, collection of laws, constitution, 'Volk Geist' and the voice of the democratic majority of the citizens of the country where you choose to emigrate that compose the concept of "our country", which you need to accept when you choose move somewhere, or GTFO. You can't move to a different culture and expect them to accept your alien values that might go against theirs. Their values hold precedence over yours.

> That leaves every minority group vulnerable

No it doesn't, this is just an empty appeal to emotional manipulation.

In most western democracies, minorities and legal immigrants have the same human rights and equal access to healthcare, education, justice system, etc as everyone else so they're not "more vulnerable" just because they can't wear a burka in public. To receive those rights, it requires them to accept and conform to the laws and values of the society they chose to move to, like the law of not wearing burkas for example, or the law to tolerate LGBT people. Not wearing burkas in public is not making the wearer more vulnerable. On the contrary, foreigners wearing burkas in public makes the locals feel uncomfortable and vulnerable in their own country.

>For example, some of the historical opinions of my fairly recent ancestors: All Jewish people should be dead;

You see, since all your arguments are just empty appeals to emotional manipulation or moving the goalposts from laws banning burkas to somehow being similar to genocide of jews, I will stop the conversation here since you're clearly arguing in bad faith. I've already covered all your points with arguments, there's nothing more I can add. If you want to accept them fine, if not, also fine. Good day.