CA rules on chains differ for two reasons that I know of from Colo and Wyoming. First, Ca drivers in general, except those that live in the mountain, don't know how to drive in snow. They really mess things up. And they don't slow down one bit. Just check Hwy 80 coming down from a ski weekend.
And just a hint of snow will close down the Grapevine in So Cal for days.
Second, the snow in the Sierras is much much wetter and heavier than in CO and WY. As a skier, we refer to it as "Sierra Cement."
It also doesn't generally get as cold, so more warming then freezing over again.
I lived and worked in the central Sierra for several years, and consider myself an adequate mountain driver, able to deal with snow. But I never go to the mountains without chains. Except maybe in July and Aug. You never know. I have driven only a little in WY in snow, and it most certainly is different. I asked the rental co about chains and they just laughed at me.
And it was true. Didn't need them with snow levels that would have required chains in CA.

CHP and the Park Service are serious about chains. The best case risk is you only get stuck, then you will get ticketed and pay a hefty fine. Rental co's don't like to retrieve their cars from snow banks. That could cost a few bucks.

If you go in May, avoid Memorial Day weekend.

Another option is to use the YARTS bus instead of driving into the park (http://www.yarts.com/). You can stay in El Portal or Mariposa and not have to get chains because the bus is equipped and driven for you (The Yosemite valley is 2000 feet higher than El Portal and therefore more likely to have snow. I was told that chain controls into El Portal from the west are unlikely). The fare from El Portal to Yosemite Valley is $7 round trip per person. The YARTS bus connects with the free shuttles and has convenient schedules. You can wait for it at major indoor locations in the valley. Renting chains costs $15 for most cars and the admission fee is $20. So for $35 that's five round-trips and no gas or chance to damage a rental car.

crisscross,
I hope you don't pay for admission into National Parks for multiple visits within a week. Entrance into most parks is good for a week. You can buy a Park Pass for $80(2010's price when I bought one) and that will get you into all of the NPS sights for a year.

Spiro --
I checked
www.Yarts.com
and, after a bit of searching (finally finding this pdf:
www.yarts.com/pdfs/140fares.pdf
found that the fare for riding Yarts includes the fee to enter Yosemite. In other words, the round-trip fare includes both the bus ride AND the admission fee.
You pay the fare each time you ride Yarts, just like you do every time you ride a Greyhound.
And you pay the same whether or not you have any kind of pass to get into national parks. That's because the NPS charges a fee on the bus company based on the number of seats on the bus
http://www.nps.gov/yose/planyourvisi...servations.htm
irrespective of who is on the bus. If a 30 seat Yarts bus pulls up to the gate at Yosemite, the NPS charges $300 whether there are 2 people or 30 people on the bus, and even if every rider on it has a lifetime pass.