Pace v. Alabama said equal protection was not sufficient. Perez v. Sharp and Loving v. Virginia require both equal protection and due process, the latter of which is now in question.
(It's all bullshit! The court will rule ideologically how they want, regardless of precedent.)
Pace v Alabama was from 1883. Perez v Sharp was a California case from 1948--an odd case to cite since it had no controlling authority outside of California.
Regardless, Loving v Virginia (1967) was decided by unanimous decision--and that's back in the 60's--just three years after the passage of the Civil Rights Act. I don't know of anyone seriously suggesting that the holding in Loving is in jeopardy today; it's literally the direct application of the 14th Amendment.
Pace v. Alabama rejected equal protection as justification. Perez, then later Loving, are relevant because they overturn that on the basis of due process as well - Perez being the first, Loving being the highest. You can't get Loving on equal protection alone; you certainly can't get Obergefell or Lawrence.
The parent asked why equal protection is not sufficient to protect interracial marriage. I answered. You don't like the answers, either:
a) Make a legal argument. To the extent you agree with this current decision, "it's old" lends it strength. But "it's old" isn't actually a legal argument, despite what the Supreme Court thinks. (That's how you know their purported theories of jurisprudence are bullshit.)
b) Make a real moral argument not rooted in made-up shit like textualism - and admit moral arguments for abortion rather than hiding behind "this is just jurisprudence."
(It's all bullshit! The court will rule ideologically how they want, regardless of precedent.)