Zombies and skeletons catch fire inside old structures

Did you create this world and house in an older version (and upgraded to the current one)? If so, it might be the same reason as MC-139017. Upon answering, the ticket will open automatically.

Yeah I created this world in earlier and have been upgrading it each snapshot.

Close as duplicate of  MC-139017?

Just reproduced this in my own world. Rain doesn't go through blocks as MC-139017, so this seems to be a separate issue.

Couldn't reproduce by creating a world in 1.13.2 and loading it in 19w13b; please reopen if you can still trigger it.

This still happens in the world I've been upgrading through each snapshot, as of 19w14a.

And it will continue to happen, since the chunks have the heightmap present and wrong. Does it happen if you upgrade from 1.13.2 directly to the latest snapshot?

It doesn't happen when going through 1.13.2→19w14b. Also tested in 1.13.2→19w04a→19w14b, 1.12.2→(1.13.2→)19w14b, and 1.11→19w14b. Just seems to happen in my really old world.

From 1.14-pre1, "Inside optimize world screen there's now an option to remove cached world data (e.g. height maps and light), so that it's recomputed on the next load". This sounds like it is related to or should fix this bug.

"Remove cached data" option in optimize world screen should fix your world, and the underlying cause of the issue was fixed earlier.