Thank you for your reply. The problem is (was) that none of the tested calendar apps accept gzipped data. I still enabled it to make downloads via browser faster. It was actually quite difficult to get the content-length correct (tried multiple different approaches). In the end, I just removed it. Now everything works with or without avast.
No browser and no calendar app had indicated any problems because of this, which is why I wasn't avare of any problems with content-length.
But as I said, now everything works.