How do tamed wolves interact with the passive mob limit?

As of the Minecraft version at the time of writing this...

Tamed wolves are not a passive mob and they do not have any limit, so they will not affect the passive mob limit (because if they were counted in the passive mob limit there would be a limit on the number you can tame.)

Passive mobs (a pig, for example) will NEVER attack you, even if you attack them.

Wolves are actually tame, meaning they follow and protect you.

Short answer:

Tamed wolves do NOT affect the passive mob limit in any way.

Actually, tamed wolves do influence the passive mob count.

If you don't believe me, you can try it. Tame as many wolves as you can (say, 15), then light only one patch of grass at night and walk far enough away for things to spawn

You can camp all day and night and nothing will spawn. The reason why there's no limit to wolves is that you can tame them, make them sit, walk far enough that they aren't loaded in memory (and then not part of the passive mob count) get some more, and walk back. But if the wolves are always near you, they count toward the passive mob count.