Question About Wiring - Hooking up New Thermostat
The black wire can be ignored

The black wire is what's termed a jumper between Rh and Rc. Some old thermostats required it since they weren't smart enough on the inside to deal with both one-transformer and two-transformer systems without such help.  You need to ignore the jumper with your new thermostat, and simply attach the red wire to the R terminal on your new thermostat, as it provides its own jumper in the form of the slider tab.