that's probably even worse, vents are supposed to be " washed" meaning rain water will wash down the pipesHave seen furnace flue type caps installed on them also.
Does the Unified plumbing Code allow installing 1/4” hardware cloth inside vent stacks on a roof to keep pests out?
Protect your plumbing system from unwanted items and debris with inexpensive pipe screens from PlumbingSupply.com®!You can get pvc screens that will fit the piping perfectly. Many use them on side wall vents

I have one that freezes without screen material. It is the main stack behind the laundry and must do just the right amount of moisture. Those copper pipe tee things helped but I still had to put heat tape around the top section. On that vent a screen would definitely not work.Could be an issue with freezing up in cold climates. Otherwise I can’t think of any issues.
Interesting, I didn't know about these. No problems here but it's good to know there's a ready solution.You can get pvc screens that will fit the piping perfectly. Many use them on side wall vents
Why would you worry if rain gets in?After my neighbor saw a crow amusing himself by dropping (big) pecans in their husks down his vent stack, we both did stuff to ours. I actually put “coolie hats” on mine so even when the rubber part started to crack, the rain shouldn’t get in .
That’s how I see it, too.Who cares what the code says if you are living there. You ain't getting inspected. Do what you gotta do.
Worst thing that can happen is you have to move/sell and you remove the screen so the "home inspector" doesn't flag you.
