MTP selected but PC doesn't show contents of external SD card
The simple way (for Lollipop and older versions): power down the Android device, remove the micro-SD, and connect it to the computer via a memory card reader.  Once you're done with whatever you're doing (copying music/photos, for instance), put the card back into the device and power back up.

As noted in comments, however, on Marshmallow, this only works if the storage is being used as "external"; if it's been "adopted" as internal storage, its contents can't be read except by the adopting device.