I can see infringing on their 1A rights.
After all, the 1A has wiggle room to infringe (crowded theater, libel, etc), as opposed to the 2A which has the key words "Shall Not" infringe.
The analogy you make is wrong.
The 1st Amendment equivalent to the prior restraint of gun control would be removing your tongue or vocal cords, because you MIGHT yell “fire!” in a crowded theater (when there was, in fact, no fire). In reality, yelling “fire!” IS permitted; however, if there wasn’t any fire and someone or several people were hurt, you would be punished for causing the injuries without justification. The gun equivalent would be to punish you if you shot someone without justification.
I wish that the 2nd Amendment was given the same legal deference as the 1st, but it isn’t. Frankly, it should be given more definite answer, because there is no wiggle room in “shall not be infringed.”