Concrete moral truths are why he shouldn't have done so.
Should Bush ask every appointee whether they've lied on their income taxes? Telling the truth is a concrete moral truth.
What about drinking? Drunkenness is one of the seven deadly sins.
How about a man who's been divorced a couple of times? No government job for him?
Bush said, when he took office, that he would base his appointments on qualifications for the job. He never said he would pass them through the Family Research Council Moral Filter.
Concrete moral truths are why he shouldn't have done so.
Should Bush make a clean sweep to remove all gays, lesbians, their friends, families, and supporters from the administration? Bush hasn't expressed any interest in doing so, in fact he hasn't even revoked the executive order banning discrimination on account of sexual orientation.
Then there is the issue of unmarried men. Do you really believe they are all chaste? Yes, unmarried men are almost all guilty of fornication. Shall we get rid of all unmarried ambassadors, or require them to forego sex during their service?
As long as gay ambassadors and unmarried ambassadors do not have sex in public or with foreign agents, it just doesn't matter.