I built a HUGE mob spawner near my house, and NO mobs were spawning whatsoever, not a single one. It was frustrating because I thought I had to take the entire thing down( after HOURS of building it). However after a little process of elimination, I killed the chickens in my chicken farm, and to my relief, Hostile mobs were spawning again. But what??! Chickens are PASSIVE mobs, don’t passive and hostile mobs have separate mobcaps?
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So passive mobs count too? I was always told that you could have a maximum of 70 hostile mobs only. The weird thing was is that hostile mobs were spawning in other places though. Probably where It was far enough away from the chickens. So I couldn’t have hit a global mob cap

The fact that villagers, passive mobs, iron golems, and armor stands take up space in an already very low mob cap (for realms especially) is a serious user experience bug. Please fix this Mojang as it's killing all of the big projects in our realm.

Agreed, this ruins the game if more than a single player is in the world.
I had bumped my tick-distance up to 12 on a private alpha server I run for my partner and myself. My partner and I were in our village which was THRIVING with probably close to 100 villages and I had built a few animal farms 20+ of each, sheep, cows, chickens and pigs. In total we maybe had 150 of the 200 mob cap just in our village.
The rest I believe went to cave spawns around the area over weeks of gameplay before we realized that nothing was spawning around us, not even phantoms.
Before that I had noticed my slime farm (which had a dedicated 5x5 chunk area where I lit up everything within to force the spawns in my farm) was not producing anything which seemed rather odd but figured it was due to not being close enough for them to spawn in.
In the end I figured out that the 12 chunk ticking distance was causing all mobs to stay loaded around our main village and even if I left the village while my partner stayed nothing would spawn, even if I traveled 1000's of blocks which effectively breaking the game since nothing could be spawned as I explored. Which included many villages that I ran into and everything else for that matter...
So far my solution has been to turn the tick-distance down back to 4, which sucks since I was using the higher tick distance for redstone projects... However this is still not a cure but it seems to at least keep things spawning around the game...

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We're actually already tracking this issue at MCPE-21856, so I will resolve and link this ticket as a duplicate.
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There is a global mob cap of (I think) 200 regardless of whether the mobs are hostile or passive. So if you have passive OR hostile animals in your world even if they are out of draw distance or unloaded totaling 200 your hostile farm won't work.