I don't know what's up on your case, but I would not jump to the conclusion that it's impossible to use tailscale with any other VPN in any circumstance.

Rather, tailscale and Mullvad will now work easily and out of the box. For other VPNs, you may need to do understand the topology and routing of virtual devices and have the technical ability and system permissions to make deep networking changes.

So I'd expect one can probably find a way for most things to coexist on a Linux server. On a non-rootrr android phone? I'm less confident.

In Tailscale you can set up an exit node which lets you access the entire internet via its internet connection.

You could set up an exit node that would let you access the internet via some (anonymizing) VPN providers like Mullvad or any other.

This sounds like Tailscale is simply setting up this exit node for Mullvad on their side and providing it as a service. So it's not like using another VPN anonymizers is impossible, it's just convenient to use Mullvad.

I just it with protonVPN on Linux with no issue.

I don't know about exit node on Tailscale because I don't use it but the rest is working absolutely fine.