Linda Hirshman notes why the resistance to marriage equality and military service is so important to sustaining anti-gay stigma:
The right knows it can't make the state punish gays as sinners, for various constitutional reasons, so it is trying to make the state deny them the closest thing it has to consecration: the sacred bonds of warriors and the sanctity of marriage. ...
It's a fight worth having, because the society rewards these secular symbols of goodness in countless unseen ways. Sure, military service is not a constitutional requirement for running for office, but it's a big leg up.
But what both do is imprint homosexuality with the core values of the right: marriage and service. Hence the cognitive dissonance. If being gay is the permanent "other", how can they also be the most admirable among "us"?