You can avoid copying other filesystems (both real and pseudo-) with rsync's "-x" (--one-file-system) option. The disadvantage of using that, rather than figuring out the list of what needs to be excluded, is the empty mountpoint directories will not get created at the destination.
You can copy the root filesystem including the mount points (and preserving their original ownership and permissions) this way:
mkdir -p /mnt/tmproot
mount --bind / /mnt/tmproot
rsync -aH /mnt/tmproot/ remoteSystem:/some/directory
The "--bind" option attaches only the single filesystem, not any submounts.
Note that the trailing '/' in the /mnt/tmproot/ argument to rsync
is significant since you want to copy the contents of that directory and not create a directory called "tmproot" at the destination. The "-H" option is important for preserving hard links. Without it, hard-linked files are treated as though they were separate files.
As with many things, the devil is in the details.