Assuming that the router tables don't change, shouldn't the path the packet takes >(hop-by-hop) be the same for the same source and destination address pairs?

There are other factors that determine which path is chosen, such as traffic.

You might find this page: Computer Networks | Longest Prefix Matching in Routersn helpful.

If it is, then isn't it a security vulnerability?

I assume you're thinking of something along the lines of poisoning the route decision to send packets where you want them to go, sort of like ARP poisoning in a LAN.

While I don't know of any specific way to do this using Longest Prefix Matching specifically there do exist methods for hijacking routes in the exterior routing space. For example: IP Prefix Spoofing Attacks.

Assuming that the router tables don't change, shouldn't the path the packet takes >(hop-by-hop) be the same for the same source and destination address pairs?

There are other factors that determine which path is chosen, such as traffic.

You might find this page: Computer Networks | Longest Prefix Matching in Routersn helpful.

If it is, then isn't it a security vulnerability?

I assume you're thinking of something along the lines of poisoning the route decision to send packets where you want them to go, sort of like ARP poisoning in a LAN.

While I don't know of any way to do this using Longest Prefix Matching specifically, I'm no expert in LPM, there do exist methods for hijacking routes in the exterior routing space. For example: IP Prefix Spoofing Attacks.