The theory I subscribe to is that tinnitus is a breakdown of the ears’ and/or brain’s noise filtering and suppression mechanisms. Long-term use of white noise makes tinnitus worse, which is a particularly cruel irony since white noise also provides short term relief from tinnitus. Active noise cancelling likely shares enough properties with white noise to cause the same effect.
Some users of noise cancellation are reporting another experience, that a sudden loud noise is perceived as extraordinarily and painfully loud, to the point that even a single incident can have long-lasting effects. This is called hyperacusis, and it is highly co-prevalent with tinnitus. Essentially, every loud noise you’ve ever heard has been pre-dampened by your ears/brain’s natural noise suppression mechanisms, and in hyperacusis sometimes this dampening isn’t applied and you get the full force of the noise - meaning that noise is literally the loudest thing you’ve ever experienced (even though it is not the highest decibels you’ve ever been exposed to).
Interestingly, one treatment for tinnitus and hyperacusis I’ve had success with is listening to audio with significant instantaneous jumps and dips in volume and frequency. The suggested mechanism of action is you’re stressing your natural noise suppression and it strengthens itself in response. Similar principle to weightlifting to stress your muscles so they grow stronger in response. Perhaps active noise cancellation is causing these problems because it’s relieving the usual stresses placed on the mechanisms and thus they are atrophying.
I avoid active noise cancellation and white noise. I have found passive noise cancellation works well - ear plugs and ear muffs, basically. They have their own drawbacks as they will affect different frequencies differently, with usual speech frequencies often being the most suppressed. Thankfully, Etymotic Research (an absolutely incredible auditory-health-first audio gear company) has the excellent ER20XS and EtyPlugs designed to reduce all frequencies equally. I can’t speak highly enough of them and how much they’ve helped me with my auditory issues. https://www.etymotic.com/product/er20xs/
Most unfortunately, it seems tinnitus is highly responsive to attention: the more attention you pay to it, the worse it gets. Obsessive researching and reading about your tinnitus can and will make it worse. Sorry. Believe me I know it sucks.