According to Christians who believe that God is a utilitarian, why is homosexuality suboptimal?

In a well-known passage Mill defends his utilitarian theory against the objection that it is a godless doctrine. He argues,

If it be a true belief that God desires, above all things, the happiness of his creatures, and that this was his purpose in their creation, utility is not only not a godless doctrine, but more profoundly religious than any other.

It’s worth pointing out that the meaning of “happiness” has changed over the centuries.

US Supreme Court Justice Anthony Kennedy explained this often forgotten sense of happiness in his 2005 lecture at the National Conference on Citizenship. Kennedy notes that while in modern times there is a “hedonistic component” to the definition of happiness, for the framers of the Declaration of Independence “happiness meant that feeling of self-worth and dignity you acquire by contributing to your community and to its civic life.” In the context of the Declaration of Independence, happiness was about an individual’s contribution to society rather than pursuits of self-gratification. https://www.dictionary.com/e/happiness/

God commanded humans to "be fruitful and multiply and fill the earth and subdue it" (Genesis 1:28; the meaning of "subdue" isn't entirely clear and might range from watching over as might a steward to outright domination).

From a strictly utilitarian point of view, biology makes it clear that h*m*sexual acts are not able to produce progeny. They are, by any reasonable definition, sub-optimal.

Strictly speaking, questions about "workarounds to that such as bisexual polygamy" are not relevant. The original question didn't ask about permissibility, but about optimality. Again, since a h*m*sexual act is incapable of contributing to reproduction, it is sub-optimal.

What about contraception? Again, it is sub-optimal in any form, even "natural family planning".

The problem with all this is that asking about optimization is almost certainly the wrong question. What is "optimized" by beauty? What is "optimized" by eating food that tastes good rather than being maximally nutritious? Does a Christian sin by never marrying? (This would seem to contradict various passages in which celibacy is commended.) Does a Christian couple sin by not trying to crank out another kid at least every year?

To be honest, I sometimes get the impression from certain Roman Catholics that the answer to the latter is "yes!". Nevertheless, even taking a more reasonable stance that Christians as a whole ought to produce an average of, say, one-and-a-half children per person (i.e. more than replenishment rate, since less is obviously not "be[ing] fruitful and multiply[ing]"), what can we say of h*m*sexuality?

Again, the first thing we can and must (if we are to respect biology at all) is that it can't contribute to this goal. From a utilitarian perspective, its value is highly questionable.

Should we argue for polygamy? Scripture, especially in the New Testament, slants heavily to treating anything other than monogamous marriage as adultery, nor is it hard to see that polygamy in any form offers significant challenges for a relationship. We live in a world where it's hard enough for two people to get along; adding a third, or fourth, or more is unlikely to improve matters. (Even in a monogamous marriage, a spouse might have to compete against his or her spouse's narcissism, but turning that competitor into a separate human adds all sorts of potential for things to go sideways.) Nor are h*m*sexual acts without their own problems, some of which are, again, purely biological in nature. Moreover, God intended for males and females to complement each other, like opposite poles of a magnet. Two males, or two females, are far less likely to be able to obtain this intended synergy, nor are they biologically capable of coming together in the way God intended.

We learn from Genesis that God wanted humanity to have "dominion over the earth" (ch1 v26), and for that end it was necessary for humanity to "increase and multiply" (v28). In other words, he needs children. Malachi makes it more specific, when he complains about the male-favouring custom of divorce; "And what does he desire? Godly offspring." (Malachi ch2 v15). This is important because the dominion over the earth was supposed to be "under God".

The Old Testament criticises a number of sexual behaviours, and the common factor in all of them (from divorce to fornication to prostitution) is that they get in the way of having godly children. In the case of h*m*sexuality and be*t**lity, of course, they get in the way of having children at all. This impedes God's intention for the world in Genesis ch1.