Podcasts partner up with ad providers. They inject ads into the episodes depending on several factors, including your location. The podcast has some say and can for example exclude some topics like politics. That catches most, but an ad can also be misrepresented and slip through.
I use Antennapod as well and they have nothing to do with it. They just download episodes from RSS feeds provided from other services.
You could use a VPN server in a smaller country. If the ad market is very small, there simply might be no ads to serve you.
I can also recommend using a swiss VPN server. The funny swiss dialect makes it hilarious.
Alternative title: "Follow these 17 convoluted steps to stay in your abusive relationship longer."