Oklahoma Republican wants to make secular marriage impossible.

[Esquilax]

Look up the history of the marriage license in America.
Marriage has always been a private contract between families. Not until the middle ages did the government start to regulate marriage (e.g. seeking permission to marry from your liege lord). Marriage licenses as a requirement was instituted in America to prevent miscegenation (interracial marriages), the whole concept of the marriage license is based on discrimination.

So what? This is neither a defense of discriminatory practices, nor of this specific proposal. At best, it's an argument from tradition, which is obviously fallacious. What's your actual point, here?

There are plenty of jurisdiction where simple cohabitation is enough evidence for marriage (common-law marriage).

And this is sufficient reason to block off certain segments of the population from an avenue, needlessly, in order to dodge the law?