VMware can remap USB and Bluetooth peripherals to the VM, but the SD card reader in some Mac models is connected via PCIe rather than an internal USB interface. PCIe peripherals can't be mapped to a VM.
You can check the connection method for your SDXC card reader by going into Apple menu > About This Mac > System Report.
In the "Card Reader" section under the Hardware heading, look for whether it has lines for "Link Width" and "Link Speed", which indicate PCIe. The other clue is to look in the USB category and see if you can find an item for "Card Reader" or "Internal Memory Card Reader".
Looking at my own models and other saved profiles I have kept, I found these models have a PCIe SDXC card reader:
MacBook Pro (13-inch, Early 2011)
MacBook Pro (13-inch, Mid 2012)
Mac Mini (Late 2012)
These newer models have a USB 3 SDXC card reader:
MacBook Pro (Retina, 15-inch, Late 2013)
MacBook Air (13-inch, Early 2015)
2010 and earlier models plus some 2011 models have a USB 2 SD card reader.
Based on the pattern it looks like when Apple introduced SDXC models in some 2011 models, it wasn't feasible to connect to it using USB 2 because it wouldn't have been fast enough, and those models were too old to support USB 3. That meant using a PCIe SDXC controller. Once USB 3 was available (starting in 2012 models) it was possible to switch to a USB 3 SDXC card reader but there was a delay before they were available, so most if not all 2012 models still used PCIe SDXC. By late 2013, Apple was using USB 3 SDXC but I haven't found the exact point at which they switched (which might vary between families).
For Mac Mini:
2010 - SD, probably USB 2
2011 - SDXC, probably PCIe
2012 - SDXC, PCIe
2014 - SDXC, probably USB 3
That means VMware Fusion can map the internal SD card reader to the VM for 2010 and 2014 Mac Minis, but not 2011 and 2012 models.
An external USB SD card reader would work for the affected models.
