Current implementations of pronoun markers allow multiple options, which for your case could be "he/they" if you're concerned about people feeling put-off by personal pronouns other than 'he' or 'she' but still want to acknowledge the agender side. In this respect they are an upgrade over the current usually mandatory "Mr/Ms/Mrs/Miss/Dr/..." field. Though people do use pronouns more often than personal titles.

I don't think it's true that the main goal of mandatory pronoun markers is cover for queer people. That only matters if whether someone passes as non-queer depends on whether they use pronouns, which is pretty specific. If cover was the only purpose of pronoun markers, nobody would use them, but people do use them because it feels important, in spite of making yourself a target for harassment.

Instead, I think the point of mandatory pronouns is people getting themselves correctly referred to with little hassle. If pronoun markers are mandatory, everybody will encounter them regularly. That means people will have lots of experience seeing pronoun markers and basing their use of language on that, so that process won't feel unfamiliar to them when they need to do it with someone who uses pronouns that don't match the gender they read them as. While currently it can be awkward to insert your pronouns in a conversation or to correct someone on their use of pronouns, in a culture with normalized pronoun markers it would be more awkward to disregard someone's pronoun markers and there is no excuse of unfamiliarity.

Because people often let their words be influenced by the path of least resistance, this would statistically push society to have way more conversations where pronoun markers are respected without hassle and fewer conversations where pronoun markers are disregarded or ridiculed. Thus, people's actual pronouns are respected more often and they're more free to express themselves, while anti-queer people lose ground because it's no longer experienced as weird and unfamiliar by the general population.

You'd even have people who would use the mandatory pronoun marker as a joke or "joke", exploring gender nonconformity in a safe environment and being more likely to become aware of their own queerness.

It seems plausible that your specific situation would become more uncomfortable, being forced to pick between exposing your identity and actively misrepresenting it, and that is unfortunate. Pretty much every social change is going to have some people disadvantaged by it, and this time it's nonbinary people in anti-queer environments who can pass as cis who are okay with using cis pronouns. That's a pretty narrow slice of the population compared to the people that benefit from it immediately, and in the long run you might benefit too when the culture and/or your place within it shifts so you feel safe to express ways your agender preferences differ from people's expectations of your cis male mask.

If you show solidarity with all the queer people that benefit from mandatory pronouns, they'll show solidarity with you when it comes to queer issues that benefit you but disadvantage random thin slices of them. They'll also show solidarity if you don't, but it would be nice of you to help out.