I'm currently having this problem, too. I borked my subscriptions flie by accident and had to readd the subscriptions, one of which has almost 1000 hour-long episodes. I had about 200 left, and it let me drag and drop the files in, but then it proceeded to try to download all the rest again, which would be a huge data suck AND completely confuse which ones I've already listened to.
This also didn't help: https://getmusicbee.com/forum/index.php?topic=28728.msg159786#msg159786
Currently the only solution is to tell MusicBee not to download the podcast at all, so you have to do all your downloads manually.
I think there should be an option like "only download future episodes" when you first add the subscription.
Update: no, it was having some kind of issue and even after trying to delete the subscription again, it wouldn't stop downloading. The only thing that would stop it was to delete the subscriptions.dat file along with downloads.dat. (Also, another subscription had the files deleted even though i definitely said "remove subscription only".)
Gonna take this to bug reports now: https://getmusicbee.com/forum/index.php?topic=28841.0