(Re)mount all network drives from fstab

You're looking for the -t flag for mount. From man mount:

   -t, --types vfstype
   [...]

   More than one type may be specified in a comma  separated  list.
   The  list of filesystem types can be prefixed with no to specify
   the filesystem types on which no action should be taken.   (This
   can be meaningful with the -a option.) For example, the command:

            mount -a -t nomsdos,ext

So, this command would mount all cifs filesystems:

sudo mount -a -t cifs

I just found out that the -t option to mount can be used in conjunction with -a, such that

sudo mount -a -t cifs

does what I need. (sudo mount -a -t cifs -o remount works as well, for remounting after permission / password changes.)