We've just - with some difficulty - had to buy our own place because although we always found a rental place that would accept our cats eventually, a lot of landlords are funny about pets (I love the positive discrimination catneuterer, wish you'd been our LL ! 
) and it was severely limiting our choices.
The last straw was having to move twice in quick succession (nothing to do with the pets, the LL wanted to sell each time) and actually considering a landlord who thought he was being very generous by saying that we could stay there as long as the cats only poo'ed indoors, not in the garden, and we'd be evicted if they fought with the next door neighbours cats at all (along with our kids).
This for about £2K a month in zone 3, and despite the fact that they were already asking for double the deposit in case of damage (which, by the way, our cats have rarely caused and when they have we've paid for it).
At that point we decided that we'd much rather be in control have a more stable home.
YABVU to say that someone renting has to somehow be in limbo and not be able to make a decent home (including pets if they want them).
Do you notice all those pet owners with their own houses having massive scratches down the walls, or poo or wee smells everywhere? Of course not, because they're largely responsible pet owners, and so are the renters!