Why does every link in my emails require me to turn off my Mozilla VPN to see them in Thunderbird?

I don't know, have you considered asking your VPN provider? You might also want to share whatever error messages appear when you have the VPN turned on. That almost certainly would assist anyone trying to guess your issue. But as VPN products routinely shield you from tracking and mask you origin using masked ip addresses it is quite possible the links you are clicking are to websites blocking those using a VPN. When you click the links in the email you receive with this reply do they work with the n[n turned on? or not what error do you get?