Does Seattle allow pet deposits? That seems like a straightforward way to handle that, and it's what I've seen when renting elsewhere.
Also I'm not sure what the new law changes. Since 2016, Seattle has banned charging extra rent for having a pet. Subsection E states: "Other than the pet damage deposit authorized by subsection 7.24.038.A, the landlord may not charge the tenant any fee for keeping a pet."
1. https://library.municode.com/wa/seattle/codes/municipal_code...
It doesn't change anything about pets, the grandparent poster's complaint is a dogwhistle.
What it does ban is shit like 'consigliere' trash disposal, where you are made to pay $50 a month for the privilege of not being allowed to use the building's dumpster. Instead, you have to pile your trash at your door, and then the landlord takes it to the dumpster. You can't opt out of this 'service'.
Oh, and the city's bill for trash disposal is still passed on to you.
Oh, and your building now smells like garbage.
(Landlords are, of course, still free to offer this as an optional paid service, which ~everyone will opt out of.)