This is not a "these days" thing. Most rights essentially being abrogated at the border is a thing we've had for many decades now. In particular, no non-citizen has the absolute right of entry, and border agents have discretion bordering on insane when it comes to not admitting people or temporarily detaining them. Worse yet, this being the case, the job attracts the kind of people who relish the petty power trip. I've seen this many times back in 2010-2011 when I was traveling regularly as a non-citizen between US and Canada.
What gives US americans the right to deny anyone access to the land they stole from the indigenous they genocided? Why do people think they are entitled to take other peoples land and then prevent others from coming too?
What gives the Turks the right to land they stole from the Tatars? What gives the Greeks the right to land they stole from the Creteans? What gives the Chinese the right to land they stole from the other Chinese?
At some point, we have to accept that the world has irrevocably changed, that people have lived where they live for generations, that resettling them all is impractical, inhumane and just not a good idea in general, and just move on and build the best world for the people currently here.
During WW1 and then again during WW2, the world has agreed to the right of self-determination. If people feel they're a certain nationality separate from what their government imposes on them, then they have a right to become their own country with their own laws and their own border enforcement. If you are literally asking what gives Americans the right to prevent others from coming, this is it.