You are correct, there are antimicrobial properties to hops. But, all things once alive must decompose. I've had tons of hops off a few vines. The debris is huge! I've not had a problem with this in my compost piles. Seriously, this is a great question. I wouldn't worry about hops in my compost pile and indeed it is truly half of the pile of debris gathered at the end of a year.
If the antimicrobial part of hops was a big deal, hops would not decompose just as rapidly as lettuce. I haven't seen that at all. I hate throwing great organic matter away. I've always found hops to decompose just fine and...uniformly?
I am trying to find if the antimicrobial properties continue after death...hops wasn't added for antimicrobial properties at all! It is strictly for taste, the bitters. Think about the medieval times and earlier! They had no use for antimicrobial properties, just taste. They had not a clue about microbes.