The Pittman-Robertson Act is the main reason we have deer and turkey to hunt in Alabama, probably the best tax money I've ever been responsible for paying.
What you say is true.
However, in Minneapolis Star v Minnesota (1987), the U.S. Supreme Court concluded:
"...differential taxation that selectively burdens the exercise of a fundamental right is impermissable." No matter who or what the special tax benefits.
The last time I looked, in this post-Heller world the 2nd Amendment now represents a protected fundamental right.
So how could you protest a 10-25% increase in this tax to pay for the medical cost of "gun violence" when you support the same special tax on guns and ammo when it benefits hunting, shooting sports and their related industries.
Certainly taxes on other outdoor/hunting products could provide
needed funding rather than placing a special tax on a constitutional protected venue.
Note: A general tax on all products, including guns and ammunition, like a sales tax would appear to be permissable.
But a special tax only on a constitutionally protected area like newspapers or guns and ammunition would be unconstitutional.
This is indeed a tough political and constitutional conundrum.