With charter schools producing better results, the argument against school choice makes no sense

Great meme. School choice is a must, additional federal $20 billion input is a must and like it or not the 4 million unauthorised students in K-12 needs addressing

We want a nation of workers, not thinkers

As long as you're quiet and don't disturb your roommates

If I'm not learning NOBODY WILL!!!

Actually, as long as a school produces good academic results, And no one is forced to go there (other than by there parents), I don't care. If they have parents that would choose that religious school, the children are going to be brought up religiously, regardless. But being allowed to choose a school whoise teaching style matches the student is the best recipe for overall success. Too many students are trapped in failing, sometimes dangerous, public schools because there parents have no choice.
Because you mentioned religious schools, I'm going to assume you were addressing vouchers, rather than charter schools.
Charter schools are actually public schools that are run privately with more flexibility, to better meet children's needs (note: these usually cost LESS per student than standard public schools). Charter schools work closely enough with the government, that it is easy to prevent them from being religious schools. Charter schools also can (and have) been shut down if there are problems with academic results or questionable finances.

Because it's always about denouncing anything related to Christianity for some people.

My kids have gone to religious schools and public schools. I've experienced the entire spectrum.

Hands down, when a religious school can produce kids with ACT scores in the upper 20s and low 30s for less than 33% of the funds given to public schools, you have to ask why. Teachers with PhDs and Master's degrees, incredible facilities, 3-D printers and CAD classes, tough security ... and accountability to the parents.

That's something you generally just don't get with public schools. Are there exceptions? Of course. There always are.

But an exception to the rule doesn't invalidate the rule.

Homeschooling depends a lot on the parents. I was pulled from public school late in second grade after a bad experience and homeschooled until I graduated. I did fairly well and scored composite 26 on my ACT a year after I graduated, but I've also seen kids who can barely add & subtract and think Adam & Eve rode dinosaurs to school.

As far as charters costing less than public schools: some do cost less, but you must remember that in most states charters are not under the same legal obligations as public schools. For instance, a charter can deny a student with special needs, a mentally-disabled student, or an English-second-language student to reduce their per-student cost; public school systems, by law, cannot turn these children away.

Government works with churches for food distribution all the time. The establishment clause does not mean that the government cannot associate with religions at all. It means that the government cannot create any laws that benefit (or detriment) any religion over another or force anyone to participate in religion. Like you said, vouchers could be used towards ANY religious school, so long as it has an acceptable academic program it does not favor one religion over another, and since school selection is a choice, does not force religious participation.