Alternatively, it's exactly because modern people would be horrified at what those three groups agree on that it is an excellent argument.

Cool! Now we have two equally credible arguments from antiquity.

Perhaps it's time to consider forming some fundamental principles and reasoning from them instead?

That would be good, except that if you told anyone about it, they'd probably be horrified.

I mean, I already believe in a lot of basic principles that would horrify a lot of people - free speech, freedom of religion, I don't care at all what someone's sexual orientation is, and so on.

So I don't see where this should stop us from trying to form principles as an alternative to arguing that something must be or must not be true because of what someone wrote down millennia ago.

The quotation is factual and avoids making an argument. I'm not sure what you're trying to refute.