I am not reading that they actually included the part about playing explicit music on the invite.I think that the entire thing is ridiculous. The disclaimer on the wedding invitation is offensive and the fact you need to place a warning about your music is questionable, IMO.
I am reading it as saying they told their DJ they wanted explicit lyrics. And then as an aside to explain that there shouldn't be kids at the wedding, added that they already included the "We love your kids, but we didn't invite them" on the invite.