Isotope pairs in different states at room temperature?
It’s not exactly room temperature but it’s probably the closest you can get to two isotopes having different states so that they can be separated by physical means:

At very low temperatures (below $1~\mathrm{K}$) liquefied helium will separate into a superfluidic helium-4 phase and a normal liquid phase containing mostly helium-3. The superfluid and the normal liquid can be considered different phases and are immiscible.