I can be used, but there are better things since it can eat away at rubber.
WD-40 is composed of 80% Stoddard Solvent (that is similar to paraffin) and 20% light lubricating oil. It's the light oil part that you have to be careful of (slippery.) Just wash it off with detergent.
The other slippery substance that you really want to avoid getting on your tires is silicone oil contained in Armor All and other rubber dressings. Particularly on stored vintage bikes.
There are two main degrading agents that attack tires and rubber parts. They are UV light waves and ozone. Both of these attack the long hydrocarbon chains of the rubber and by breaking these chemical bonds, shorten the molecules with resulting loss of elasticity and other problems.*
Tire manufacturers add two primary sacrificial protectants to the rubber. To protect against UV, they add carbon black. This is why tires don't come in designer colors to match your paint. The carbon black will turn white/gray as it absorbs the UV and dissipates the energy as heat. Thus the basis of rubber parts turning gray as they age.*
To protect against ozone, tire manufacturers add a wax-based sacrificial protectant. The ozone attacks the wax and depletes it. As the tire rolls, additional wax is forced to the surface of the tire. This is referred to as "blooming". This blooming refreshes the surface wax protectant. A tire that has not been flexed will have the wax depleted by the ozone and thus begin to degrade and suffer "dry rot".*
The silicone oil in Armor All and similar products actually dissolve the wax and can be the cause of premature tire side wall cracking/failure. It is rumored that some tire manufacturers will not honor warranties on failures caused by silicone-based products. A tire dressing should contain a UV protectant to bolster the efforts of the carbon black and preferably not contain any silicone.
Since I don't know the exact chemical composition of WD-40, and in fact it is considered a "trade secret", I will merely note that volatile organic compounds ( VOCs ) will dissolve waxes. WD-40 contains VOCs.
If your aiming to clean the tires, use armourall cleaners. In my experience they work amazing to clean and shine the tires. Rims I always do with a wash mitt, cleans brake dust nice and easy. Just be sure to use two seperate buckets for cleaning the tire and the mitt!