Don't give them "your" email. Give them a mail alias, which I am sure as a privacy conscious person you already have, and you are good. They also recommend to do so themselves.

However, the most important argument here is not the fact that they are legally bound to those privacy commitments (they are), but that their business incentives are fundamentally incompatible with tracking users. For a very niche business with an extremely narrow and homogeneous user base, if they would get caught doing so, it would be game over. The privacy pass feature is available if you don't trust, and you can verify since everything relevant happens client side.