When you claimed, "I agree that politicians need to be more consistent. That doesn't mean masks don't work or the virus is fake," you presented two options whether you knew it or not. On one hand, you have the sensible answer: "politicians need to be more consistent". On the other hand, you presented an option that no notable person has ever held in its entirety: "masks don't work/virus is fake". It is true that you didn't present this in the form of a question, but you answered it in the form of an issue which has two options.
Technically it may be considered more of a strawman than a false dichotomy, but I think it resembles a false dichotomy.
At the end of the day, I think the underlying error of your statement was that you said "that means". I have never heard of anyone claiming that the need to more consistent politicians also requires one to adopt the additional beliefs that masks don't work/virus is fake. You also did not present any such evidence.
Look, this isn't as big of an issue as this seems as it relates to the virus. I already agree with you that politicians need to be more consistent, that masks can work, and that the virus is real. We may disagree on the specifics (e.g. the circumstances in which masks work or should be worn), but not on the basic question.