In the US, it's very common to discriminate against pet owners, either by not renting to them or by requiring extra deposit against pet-induced damage -- or even worse, just demanding extra "pet rent".
In the province of Quebec you can specify a "no pet" rule in a lease. You can even be more specific and allow for a certain number and type of animal (e.g. max 2 cats, no dogs).
There's a lot of stuff you can't discriminate on, but animal ownership isn't a fundamental right.
In Ontario, the law stipulates that a land owner may not restrict leasers from owning a pet, unless the pet runs afoul of other stuff (like if they somehow interfere with another leaser's ability to live a reasonable life). But everyone still puts the 'no-pet' clause in the contracts.
I don't know about the US, but in Canada I think it's illegal for renters to discriminate against pet owners. Many still do however.