The Constitution gives us the right to bear arms, and our constitutional rights come from G-d.
The Talmud guarantees a right to self-defense (Sanhedrin 72b).
Maharshal paskens that one can have a vicious dog in an area of danger; therefore, for self-defense, one can have an object of danger. Rashi (on Shemos 22:1) says that a burglar has no blood, therefore, it is not retzicha to kill an intruder.
Furthermore, Rav Shlomo Goren and Rav Meir Kahane were ardently pro-gun, even allowing one to use them on Shabbat to avoid danger.
The objection you were pointing out was a woman wearing a gun decoratively, like a man. For self-defense, anyone can use a gun and lo yilbash doesn’t apply there.
I don’t know enough about how they learn to make a statement on that. I am much more familiar intimately with YU’s learning, since they make it available to the world on the internet.