According to this page SD cards drive and or release the DO line synchronously with the sclk line:
In the SPI bus, each slave device is selected with separated CS
signals, and plural devices can be attached to an SPI bus. Generic SPI
slave device drives/releases its DO signal by CS signal asynchronously
to share an SPI bus. However MMC/SDC drives/releases DO signal in
synchronising to the SCLK. This means there is a posibility of bus
conflict with MMC/SDC and any other SPI slaves that attached to an SPI
bus. Right image shows the drive/release timing of the MMC/SDC (the DO
signal is pulled to 1/2 vcc to see the bus state). Therefore to make
MMC/SDC release DO signal, the master device must send a byte after CS
signal is de-asserted.
So just sending a dummy byte to the SPI after raising the CS line high should work. The site above has a timing diagram of the SPI bus when raising the CS line high on the SD card.
Also, it is a good idea to make sure that on power-up/card-insertion the microcontroller negotiates the use of SPI mode with the card. These details can be found here
In summary, it should be OK to share the SPI bus with multiple peripherals as long as the above precautions are taken.