made the case for racial profiling

No.

- When you are "making a case" for a policy, you are making an argument that the policy or practice is justified.

- "Racial profiling" is when police look at someone's race to determine how much of a risk they are to commit a crime.

So the writer of this article is claiming that the "Republican" was making an argument that using someone's race to determine how much of a risk they are is justified.

Thank you.

Another question:

Does "barely making it and, let’s say, comes out of Sweden" mean "almost unsuccessful and, for example, (she, the old lady) is from Sweden"?

PS. "who’s central casting for profiling" is also confusing to me.

It's been said before, Trump has a way of mangling words into some sort of Trumpspeak. He might not be the best case study for mastering control of the English language. Still, here's my two cents.

'Barely making it' is probably in reference to the age and the fact that she is in the wheelchair. Trump is implying she could hardly be a threat if she can barely move and is close to death,

central casting could be interpreted as 'prime subject matter' I suppose in this sense. Trump states that this man should be a prime target for profiling, due to his looks (he 'looks' like the guy that has just been captured after all).

- "barely making it" is an idiom that means "barely surviving". The suggestion is of an old lady who is frail and weak (and thus not a threat).

- "comes out of Sweden" is painting the image of someone who doesn't look like they come from the Middle East (the implication being that someone from Sweden is not going to be a terrorist).

- "Central casting" is a phrase used in the Movie Industry. It is a place to find people who fit a certain stereotype. If you are making a movie that has a Native American village and you need people who look like Native Americans to be in the village, you would go to central casting to get actors to play these parts.

The point is that there are people who fit the stereotype for Middle Eastern Terrorists (i.e. they would be the type of people you would get from central casting to play the part of terrorists in your movie).

He is arguing that the police and security guards should be focusing on people who look like stereotypical terrorists, rather than worrying about an old, frail, White woman in a wheelchair.

I am just helping you understand the English. I will leave the politics to others.

Thank you.

Does "for profiling" mean "for analyzing/studying"? Or does it mean "because of his/her characteristics"?

The phrase is "racial profiling". It means attempting to use someone's race, or racial appearance, to judge how likely they are to be a criminal or a terrorist.