I had to deal with this problem when I was chairman of a Christian school.
Most of these schools have an enrollment contract which states something like “We recognize that Little Sally will be taught the Christian religion, and we contract not to deny or disparage its essential tenets at home”.
Raising a child in a home with unmarried parents or with two persons of the same sex engaging in sexual relations while proclaiming in public that it is normal or blessed by God is considered by most Christian school governing bodies as “denying or disparaging” the Christian religion.
To be fair, most of these schools are more likely to accept a child of heterosexual fornicators that they are a child of a same-sex couple, but then there is that whole abomination thingy to deal with.
Most of the time, when a homosexual or lesbian couple brings their child to enroll at a school which teaches that the couple is an abomination, they are using the child to attack the fundamentals of the school, which fundamentals they despise.
It’s not “punishing the child” to refuse a contract signed in bad faith.
I am guessing you are familiar with the very meticulous and highly researched work and persecution of pastor Scott Lively regarding the origins and end goals of the modern LGBTQ campaign.
The history is heavily researched by multiple historians, with practically impeccable historical citation’s, very well done, but of course is near universally attacked —
https://www.scottlively.net/scott-lively-books/the-pink-swastika/the-pink-swastika-files/
It is also interesting with historical perspective, after a strong wave of Darwin based secular humanism swept Europe in the mid 1800’s, it was followed by a violent feminist/sodomite movement, which would itself not only back the socialist toralitarians across Western and Central Europe, but also lend itself to the socialist/communist Bolshevik revolutions in Russia!