At least around me, it's pretty easy to get into one due to enrollment not being very full in most if not all. They will of course give automatic enrollment for anyone in the parish, but I can't really argue with that since these schools are usually subsidized by the parish and local dioces.

You need to test to an academic standard of course, as they definitely want to keep the bar rather high. So they won't take all comers. But if you are either just starting out or come with an academic track record/high percentile test scores you shouldn't have much of a problem at all. When I went even 30 years ago there were plenty of low income kids who were not academic superstars. The only real metric that was universal across the board was the requirement for involved parents.

I'm sure other areas are different, but Catholic schools in my region have really suffered in recent years with a lot of them closing down.