Neither opinion should be an offense, yes. Its whimsy, some people say there are hundreds of genders, hence its pseudoscientific.

You're asking the wrong questions in an attempt to make it sound more ridiculous than it is. It's not about reaching some scientific consensus of the exact number of genders that exist.

You said it yourself, gender is a social construct. So why limit it to just two and exactly two? Because you want to dictate who and what everyone else can be?

If gender is a social construct, and you want to be entirely objective, then there are zero genders. Gender is just a myth. From a subjective point of view, gender describes how a person identifies, presents, and expresses oneself, in which case there are as many genders as people identify as.

The "scientific consensus" is that there are at least three biological sexes, and that sex is a spectrum in which male and female provide the two polarities, and intersex describes anything in between. Gender, on the other hand, being a social construct, is more in the realm of sociology, and not the place for making concrete scientific assertions that impose extrinsic limitations on individual expression. From the perspective of psychology, an individual's gender identity should be respected, acknowledged, and affirmed, because this has been shown to have the best outcomes out of all the treatment options.

As far as "finable offense" goes, you're really missing the point. Average Joe Schmoe at the local dive bar isn't going to get a ticket for saying there's only two genders. He'd just be wrong, and people might avoid him, or maybe even argue with him, but he's not going to get fined over it.

If you're entrusted as a public servant in a position of authority, with potentially hundreds or even thousands of people whose day-to-day lives depend on your decisions, then you're responsible for the ways in which your words impact those people's lives, you should be held to a higher standard, and you have a duty to govern your personal conduct accordingly. Someone in such a position making comments that deliberately exclude a vulnerable minority group and invalidate their personal identities causes harm, and shouldn't be treated as protected political speech because it's not done in the capacity of a private citizen but as a representative of the state.

but you think it righteous to punish someone for a wrong answer?

Why do you believe this is what’s happening? What parts of what this guy had as evidence against him that you think should get protected as free speech? Quote something specific that was raised as evidence

If they arent harming you, what do you care?