Who cares about the career aspirations of a few preachers?
Actually though, this objection highlights the core issue. The gay exclusion policy is a statement that LGBT people are not full citizens, not really full human beings. Religious leaders claim in their various traditions to be able to affirm or deny the humanity of some, with God's force behind them. A diverse secular polity says "no" -- all humans are created equal under the law, whatever some peoples' understanding of God might tell them. If some people don't want to believe the full humanity of LGBT individuals is allowable in God's sight, that's their right. But they don't get to impose their cramped god on the diverse, fractious whole of society.
None of us get to impose our values on the whole.
I'm not thrilled with the idea of gays choosing to join the military either. In 1993 when the DADT policy was being hatched, I handed out thousands of these stickers at a gay march on Washington.
I think I understand the attraction of the military to some terrific people, gay and straight. For some, enlisting promises escape from lives with few prospects, possibly even from unhappy parental homes. There may be material benefits, but also, in our sleazy consumer culture, the military seems to offer a structured alternative, grounded in a morally satisfying posture of altruistic patriotism, "defending your country." That's fine until "service" turns out to mean becoming a killer for a decaying empire and living (if lucky) with the physical and spiritual consequences.
I think that's a terrible fate, for anyone, gay or straight. But I don't get to impose my values on the society any more than should the dissenting preachers. LGBT people are full and equal citizens; if folks want to join the military without hiding their orientation, they should be able to.
H/t to Tobias Haller for pointing to the unhappy chaplains.