That is definitely not normal. We expect modules to influence each other, when they are connected by a wire, and no influence without a wire. There is a reason why wireless modular hasn’t been invented yet: nobody wants it.
Jokes aside: how do you supply your setup?
If by chance you are feeding some “5V” into the USB-C, the 5V rail may be weak. The 5V rail supplies most (if not all) LEDs, so turning one on or off via the Env mode switch changes the current that is drawn from the 5V regulator. And that can change the actual Voltage on the 5V rail, if it is underpowered (weak). That in turn may (if the 5V rail is low enough) change the 3.3V on the ESP board, wich acts as a reference for the analog outputs.
This is just a theory, but kevinjwalters has documented the behaviour of the 5V rail in various supply situations here and the datasheet of the AMS1117-3.3 should explain the rest.
Edit: Datasheet says the AMS1117 needs 1.1-1.5V more input than output, so the 3.3V are in trouble, if the 5V rail drops below 4.4V, which happens if the input at the USB-C is below 4.7V, which can happen, especially with long cables in USB-A sockets (5V wall warts with a permanently attached cable compensate for the voltage drop in the cable at higher currents, but at a USB-A socket they don’t dare to generate overvoltage).
So we could do the Buchla thing and declare this a feature (“wireless modular”), saving you lots of cables in making microtonally generative patches… 
Or: use a good power supply. I’ve had good experience with a modern smartphone charger (USB-C, 20W); the power module will try to get 12V, but is also happy with 9. Or via the barrel jack: 9V or 12V, at least 1.5A.