Do any airports have runways or taxiways that cross active rail lines at grade?
There is at least one:

In Gisborne, New Zealand, there is a freight rail line which crosses the south end of runway 14/32 at Gisborne Airport (GIS). It appears to still be an active line for freight (logging) haulage, as well as occasional passenger excursions.



Image source: Google Maps, plus own annotation.

This article has some additional pictures and info as well.