If NRaas mods are in play, then StoryProgression can be used to disallow species or other groups of sims by way of SP > Lot Options on each individual lot you wish to restrict (NRaas GoHere is required for the mod's Lot Options restrictions to be honored).
Or, this time if GoHere is in play, the lots or venues contained within can have door (gate, archway) locks set on them that restrict animals from entering. In this scenario, the area to be restricted has to be fully enclosed either by way of fencing or walls and doors. Currently this method does not extend to sims who might be carried in like the SP way does, so in theory sims could still carry their kittens and puppies into such a restricted area and set them down.