I am also not up to date on Jellyfin security issues but the biggest one I care about is that its clients don’t support OIDC. There’s a neat plugin for OIDC, but without client support it only works with the web client and I’m not a fan of leaving login pages open to the internet.
Honestly, the easiest thing to do is put it on a mesh VPN like Tailscale and connect their streaming device to your tailnet. If they’re non technical parents then if their TV OS doesn’t support Tailscale, you can pick up a Walmart brand ONN streaming box for <$50 which supports for Tailscale and Jellyfin.