Problems running Wireguard as container and Tailscale on the same machine

I access my seedbox via Tailscale-only (all other external traffic is firewalled).

On that machine, I use the docker-compose project which routes all container traffic through Wireguard container (network_mode: service:wireguard), all that works fine.

The problem arises when I up/down containers after a config change, when Wireguard container restarts, it probably does something with iptables which makes me lose connectivity to any of my container web UIs that I access via Tailscale.

This is what the container does on exit:

Is there a way to prevent it from messing up with iptables rules that impact Tailscale?