There's a lot of daylight between "recommendations for some higher age groups, no recommendation for lower age groups" and "recommendation against for lower age groups." The international recommendations cited above seem to be in the former category. Florida's recommendations seem to be in the latter. This might make them an outlier.
Whether it makes them conspiracy theorists is another matter. If their position is sound, well, sound positions can be embraced for sound or unsound reasons. If their position is unsound, of course it will be for unsound reasons. So whether they're called conspiracy theorists matters much less than their reasons.
What are their reasons? They appear to cite a large relative increase in myocarditis risk in younger men. A statistically literate response would involve asking what the absolute increase is... and the proper place to reckon with relative comparison would be vs the unvaccinated infected:
https://www.heart.org/en/news/2022/08/22/covid-19-infection-...
I would absolutely recommend anyone wondering about a specific vaccination consult with a doctor or two (I do this and have had a certain class of vaccines contraindicated). But no red flags from medical pros on this one for me, and personally, even as a man outside the high-risk age groups, I can't remotely see a reason for assuming myocarditis would be a reason for avoiding the vaccine. As far as I can tell, it's almost on the order of your lifetime chance of being struck by lightning, and the chance of developing myocarditis from infection is significantly higher.