I think if a foreigner has no prior criminal history, they should be given a path to citizenship. If they do have a criminal history, then I think it should be case-by-case because I don't think "one size fits all". And I don't think families should be split up.
As far as where fans stand ideologically, those of you who are right-wing should know by now that Star Trek is left-leaning. So if you're fuming about "Oh my God! Look how they portray ICE!!!!" that's what I call "mock outrage" because you had to have figured that's what would happen. What exactly were any of you expecting? Don't kid yourselves.
When they time-travel into the past, a crewmember being caught by the authorities is nothing new. Kirk was caught on an Airforce Base and thought to be a spy. Chekov was caught on a Naval Vessel (the Enterprise) and thought to be a Soviet Agent. Now it's Rios' turn.
Which transitions into my being able to say I love when Seven and Raffi run from the cops and beam out when the cops think they have them. Reminds me of when Security chased Kirk, Gillian, McCoy, and Chekov in TVH. "Freeze!"
The TOS Movies liked having a maverick crew. The crew in PIC, made up of Ex-Starfleet and Non-Starfleet personnel (until some of them became active Starfleet again), is made up of mavericks as well.
Archer was caught by the Nazis.
B'Elanna was caught by meth making white supremacist hillbillies.
Entering the country illegally is criminal.
Overstaying a Visa is illegal.
There is no "easy" path to citizenship available after you have burnt those bridges.
The problem with dumping Rios at a bus station in Mexico, is that the Mexican police are also going to be miffed that he can't prove that he's Mexican. The US Government can only deport him to a country that will accept him?
The Secret Service might get involved, because they track time travelers irl.