There are several points that should be considered here.
1st -- you say that "It seems to me that such a god is unlikely to concern himself..." etc. This leads to a bigger question -- whether God concerns him/her/itself with us at all. Either he does or he doesn't. If not, you are expression the position of Deism. From such a perspective, of course God would not be concerned with gays marrying, because God from such a perspective does not care about marriage at all.
2nd -- You say -- "It seems to me..." -- that fact is God either does or does not care, regardless of how it seems to any of us. So for any of us to say "it seems to me" is just an expression of our opinion about an entity, which if existing, is farther beyond us as we are beyond your typical bug.
3rd and finally, IF God DOES care about us on the personal level (the non-Deist perspective), THEN in fact God may be against gay marriage.
(a) If God cares about us, he will communicate with us.
(b) God will communicate various things, but some of those things are rules about how to live our lives.
(c) The Christian biblical prohibition against gay activity is usually listed along with other practices such as -- don't steal, don't drink alcohol to the point of drunkeness, and so forth.
(d) If in fact such writings really are transmitted from God, then it is not reasonable for us to "pick and choose".
Therefore, it is perfectly possible that God may be against gay marriage. Whether one believes that in fact God does care or not, and whether one believes that if God does care that in fact the biblical writings are authoritative, is a personal consideration that each person must individually make.