As an owner, is the property purely investment? If so, maybe consider allowing pets as many good, long term tenants have a dog or cat, but be sure to include a pet clause in the tenancy agreement. For example this would include limiting the pet to the one named, covering any damage caused and having carpets commercially cleaned at the end of the tenancy.
If the property is one you wish to move into in the future, then you may decide that tenants with pets are a no go. Or maybe you decide you don’t want pets in your property due to previous bad experiences. Asking for a pet reference is a good idea either way.
Ultimately it is the owner’s decision and until the government changes yet another law, it will remain the owner’s decision.