> Does that make America “a nation of immigrants?”

The vast majority of Americans are immigrants.

> Is it a defining characteristic or an incidental one?

Is this even a question? Again, the vast majority of Americans are immigrants.

> I wouldn’t say that’s a defining characteristic that should define our future immigration policies.

You can try to move the goalpost as far as you'd like and blow as many ignorant and ill-informed xenophobic dog whistles as you'd care to blow. You cannot outrun the fact that the US is a nation of immigrants.

I simply read your post to make it make sense. That is, you’re saying “America is a nation of immigrants” to refer to some articulated principle—like free speech or property rights—that should compel the electorate to adhere to some policy going forward.

If by “nation of immigrants” you mean merely the fact that most Americans have immigrant ancestry, your original post makes no sense. Why would that incidental fact have any bearing on what America’s immigration policy should be going forward? Mere accidents of history don't compel a democratic republic to maintain any particular course.