Javascript tags in content mess up RSS feed

Hello.

Recently my RSS feed and thus Feedburner as well stopped working.
I checked and validated the feeds. Both, the original source and Feedburner were not valid feeds.

It showed me that some script tags in my blog posts were causing the issue.
Those script tags came from Google Adsense as I had inserted it into my blog posts directly.
Once I removed Adsense from my blog post content and have it only in my sidebar my feeds are valid again and working.

I KNOW that there are people who use Adsenese AND RSS without any issues.

Why doesn’t it work in my case?

I know one shouldn’t inster script text into the content, but what else can I do?

Anybody else ran into the same issue before?

Here’s my blog for reference: http://zoomingjapan.com/