I funnily had the same use case. Two different jellyfin servers for complete separation. Both routing through gluetun. The reason this doesn't work is because the network mode setting you have basically makes all three containers operate in the same network. Meaning if one binds a port the others can no longer bind the same port. Their different hosts but all sharing one network and port range. To expose the ports you can move that ports setting from C1/C2 to the gluetun service definition. This'll still work because when C1 binds to 1234 it'll be reachable through the gluetun service.

Note: as mentioned if C1 and C2 cannot use the same port if you also want to have service gluetun set. More likely than not you start C1, it binds to the port, start C2, it tries and fails to bind to the port and crashes. I fixed this by making one of my jellyfin containers use a separate port. If you can't configure the ports of your services then there's no real recourse FWIU.

On mobile so you'll have to forgive format jank.

It depends how each image handles ports if C1 has the ports set up as 1234:100 and C2 has the ports set up as 1234:500 then:

service:

gluetun:

ports:

 - 1234:100 #c1
 - 1235:500 #c2

[...]

Will solve the conflict

Sometimes an image will allow you to edit it's internal ports with an environment so

service:

gluetun:

ports:

  - 1234:1000 #c1
  -1235:1234 #c2

c1:

environent:

- UI_PORT=1000

[...]

When both contsiners use the same second number, C1: 1234:80, C21235:80, and neither documents suggest how to change that port, I personally haven't found a way to resolve that conflict.

The port number on the outside doesn't have to be the same as the port number on the inside.

You can just change the port directly on the application for one of them.