While I agree with PP's points on safety, since you are a parent I'll give you the benefit of the doubt that you aren't trying to bypass safety but are just asking if the height issue is legit so you can properly set expectations with your kids.
My DS is also 3 and 37" so I understand where you are coming from. For them Cars is huge, its like telling a 5 year old girl that they can't go see the princesses. Because Cars is such a little boy thing I kinda wish they had designed the ride to be safe for smaller kids like most of the rides in Fantasyland and Toontown. But they didn't, so its more of an older kid/adult ride and a lot of little cars fans will miss out.
I'm hoping DH and I will get to do single rider without my DS noticing we're gone. We'll probably take turns sneaking away while the kids eat at Flo's V8 Cafe. Maybe you take him on the other CL rides (Mater's and Luigi's) while your DD is riding RSR? There are also some shows on the street, and its seems like plenty of ways to immerse them in CL without riding RSR. I know it will take more than a gift shop to keep my DS occupied long enough for the current RSR lines. Also, I believe 37" is tall enough to ride Autopia at DL, so at least you can play up that "driving" experience to make up for it.