Keeping this in consideration, what years did tractors have steel wheels?
When the first tractors arrived on farms in the 1890s, they were equipped with steel wheels, and it took 40 years for inflatable rubber tyres to arrive.
Subsequently, question is, why don't Amish use rubber tires? Rubber tires are seen by the Amish as something "which could promote sloth, luxury or vanity" and thus "is strictly prohibited" (Source), as I understand it anything that makes them dependent on the outside world, or will distract from their family values is not allowed.
Also question is, what is a rubber wheeled tractor?
A tractor, fitted with large rubber-tired wheels, which can travel comparatively fast over rough ground.
Why do some tractors have metal wheels?
For the Old Order Mennonites can use their tractors in the fields and on the road for agriculture purposes. They kept the steel wheels as long as manufacturers offered them and eventually starting making their own. The idea is so that tractors won't be used for personal transportation.