Supposedly because it's considered hypocritical of Republicans to be involved in activities that they, as a group, oppose, whereas Democrats are sooo tolerant, loving, and accepting of all lifestyles (unless you're a Christian and/or conservative).
I don't know that the Republican Party formally condemns homosexuality (other than the religious right wing of the party). The difference is that the GOP does not believe that this particular lifestyle should be given special treatment in public policy, or officially declared "normative."