Why is the speed of ideal gases mass dependent while the kinetic energy is not?
As the mass increases, the velocity decreases, yes that is true. But how does the kinetic energy remain the same? 

The increment in the mass is balanced by the decrement in the velocity. In other words, the velocity changes as the mass changes in such a manner that the kinetic energy of the molecules of the gas will remain to be same no matter what. It's something like the multiplication of two variables always giving the same constant value. Keeping in mind that this is true in an ideal environment.