So we shouldn't squawk when homosexual marriage is voted down by popular (viz. majority) vote?

I would say I'm referring to God's law as revealed in the Bible, the Decalogue primarily, though certainly any of God's moral laws as laid out in the Bible would apply.

The purpose of any man made law is I'd say to restrain people from harming society or one another (and more often themselves, though I'm not sure I'm completely on board with those sorts of laws). If we as Christians want to take God's laws, say the notion that being a homosexual is immoral, and incorporate that in our own man made laws as Uganda has done (though I'm not sure if their reasoning is religious) then I think we're on shaky ground. While that would I suppose be an opportunity for a second use of the law, is there a place for that in man's laws? Is the purpose of a law on the books to point to righteousness? I don't think it should be.

I certainly think that there is some overlap of God's righteousness as revealed in the Law with our own civil laws. They agree on murder and theft and the like, and I think that's “Utilitarianism”? If so, then yes. As a society I think all we can strive for and hope to succeed in is to pass laws that serve to provide a common moral code that we can agree on in the majority. Where that lines up with Biblical laws/righteousness I think is just a bonus. If our purpose is to try and make people “de facto”Christians morally then I think that's where we go wrong.

This.

I would love to see this unpacked. A number of questions surface in my mind when considering this paragraph in any context, but especially in this particular context.

First, although not immediately related, what do you mean here by “God's law”? Are we reflecting on natural law? Ceremonial law? Civil law? Moral law (a more specific iteration of natural law)?

Second, what is the purpose of any law? You quoted Romans 3:20, which in its context is likely referring to the “moral law” as best summed-up by the 10 commandments, but specifically speaks towards what has been called the “second use of the law” in the parlance of Biblical scholarship (Second use of the law – making error known and defining right/wrong for the purpose of directing the unrighteous to the righetous one). Historically, there have been distinctions between this “use” of the law and additional “uses” (First use – serving to restrain behavior; Third use – serving as a guide for proper living). Is there any overlap of these three uses of the “law” (as understood here) with our current civil understanding of “law”?

Third, you seem to be leaning against what would fall under the “Second use of the law” category from above. Fair enough from my perspective. You do state, however, that “What is righteousness? Well I suppose it could be defined as Biblical or Godly morality.” Given this definition, what other basis do we have for law so that we aren't “[trying to] cloak others with it by making our own laws some reflection of God’s Law”? Is this where we invoke a categorical imperative? Is there such a thing? Do we seek a pure utilitarianism (and concede that it doesn't truly provide “morality” but simply an answer to “what is better”)?