Plessy didn’t establish a test, it merely upheld a statute itself setting that guideline.
I don’t think that race discrimination by non-government actors was the target of the 14th Amendment, nor do I think that all varieties of government discrimination were targets of the amendment.
As Tom and I said in WKTC?, the Supreme Court justices who decided Brown didn’t think that the 14th Amendment was meant to address this question either.
