I openly criticise Dubai for their slavery, I refuse to visit Dubai for that reason alone. However, I refuse to say that Dubai is objectively less moral than the United States because morality is relative to the culture that defines it, in the same way I refuse to say that sushi is objectively better than pizza (despite sushi obviously being superior to pizza).

You may assert it but morality is not defined by or measured in outcomes, morality is a cultural product. If your moral system is not objective, if your moral system is a culturally-influenced personal belief in what is right and wrong, it is totally incoherent to say that Saudi Arabia has not made moral progress or that they have not used "modern thinking" because by their moral standards they have, and by their moral standards you (and I) are the immoral.

If you'd like to compare the United States to Saudi Arabia on human rights, press freedom, education, crime, freedom of religion, gender discrimination, do that. They have outcomes that we can measure, and don't worry, they're influenced by morality, so you can still pass judgement.