4 bit SD card - sharing the interface?
You could probably gate the clock, but you'll need to be very careful about the timing relationships between the signals. You may have to find a gate with a very low propagation delay for that to work, and you may run in to issues with pushing the clock as fast as possible.

Another option to consider might be using a pair of bidirectional bus switches, and delaying all of the signals by the same amount. This might actually be your best bet. Several companies make fast FET based bidirectional bus switches that can pass high speed signals with low propagation delays. One 8 channel switch for each socket would be perfect. The switches are usually 5v tolerant, don't have ESD protection diodes to Vdd, and they clamp passed signals at Vdd, so they can be used for fast level translation.