What is the potential for a FUSE mount to destabilize a Linux server?

I have used FUSE with both sshfs and HDFS. sshfs seems to be very reliable, I've not seen a panic or hard crash at all. HDFS otoh has caused numerous crashes. This was investigated tuned, so long as we don't see heavy usage of hdfs everything is stable.

I've seen sshfs's host systems disappear with no ill effects. HDFS caused all kinds of problems. This leaves me with the impression that sshfs is quite stable.

I would suggest testing lots of I/O and see how sshfs handles it, I expect it would handle it like a champ.

It appears (correct me if I'm wrong) that you're considering installing FUSE-sshfs on your server. You might be confused about the way it works: FUSE-sshfs should be installed on client machines. The server does need any more than it already has: the SSH server.

The "potential for a FUSE mount to destabilize a Linux server" is "some".

It will pay to understand the nature of FUSE. FUSE it not itself intrinsically unstable. It is (relatively mature) kernel code that provides a way of running user space 'drivers' for various filesystems. It is intended for testing or 'toy' filesystems, or those that don't 'belong' in the kernel, or those that are still in flux, i.e. that themselves might be unstable, however given that the driver runs in userspace, any problem in the user-land driver code is somewhat isolated from the kernel. It is in this way arguably more stable than running immature code in the kernel.

The exact stability depends more on which FUSE module you are using. I've used sshfs a little and have never once had a problem with stability. The filesystem stops responding if I lose connection to the SSH server, but that's expected, obviously.