That's something I was wondering. Why just the most protective stuff? Why protective stuff at all? I remember that some families were buying armor for their relatives who are soldiers (and that some of it wasn't as good as the stuff they were being issued anyway, but I digress), so this would prevent that...for...some reason?
I don't personally believe that it is always productive to seek a reason, that is, an explanation that assumes that people always behave as rational agents. There is just too much evidence that people don't work this way. Most people are not only non-rational but outright irrational pretty much of the time. There is also a class of people who are more often rational and are attracted to situations where they can use their reason cynically to manipulate others' irrationality. One of the biggest draws is politics.
Short answer: this is probably all imagery, and there is no rational agency at work beyond the purely cynical and manipulative.
Protective stuff, as you put it, is in an interesting category. Unlike arms, it is not protected by the First Amendment. In an alternate universe, perhaps the Fourth Amendment is interpreted to apply to this, but it hasn't.
I do not agree with Republicans who say that Democrats are hell-bent on taking away your safety. The idea of an Obama ban on guns is particularly ludicrous, especially as IMO, Obama has been the most conservative President since Eisenhower. There is no evidence for this.
However, there is evidence that this attempts on banning have been done a lot, largely for imagery. Weapon bans are interesting. They are explicitly based on imagery, formerly that of the "Saturday Night Special" and more recently the "Assault Weapon" ban. The name itself is pure imagery, exploiting the fact that Americans are too stupid not to tell the difference between the vaguely defined "Assault Weapon" and the properly defined "Assault Rifle," which has been strictly limited since the 1930s and got more restricted during Reagan. An assault rifle has only been used in one murder in the US since the 1930s, and that was by an off-duty cop who had access to them anyway. Since the 1980s, civilian (assuming that police are not classified as civilian) ownership of new assault rifles has been banned. They are pretty much collectibles to be shot under supervision at ranges for fun. That's as opposed to, say, France. I have been assured by French people on this forum that they are fairly common and easy to get, though outright illegal for civilians to possess, unlike the US where they are legal with Federal licensing (but only old ones).
So the "assault weapon" category specifies things that are purely cosmetic, thus, imagery. They do not bear on the effectiveness or lethality as opposed to the category of "hunting rifle" in any meaningful way. "Assault rifles" tend to have scary black plastic instead of warm wooden stocks with pictures of bucks on them. Pure imagery. But there is a risk that, as laws get tested by more and more courts up to the supreme one, that you'll get a judge who knows something about firearms and who is clever and cynical enough to make use of the image of greater lethality in a ruling or opinion.
Body armor has no such legal protection, and so it has been a favorite for image-based political efforts since it became widely available in the early 1980s.
I remember some fellow progressives during that time suggesting body armor as a better idea for protection than handguns. Some even fantasized that by now, body armor would be considered a fashion accessory, so there's imagery there as well, and I have seen some pink handguns for sale. It's not a terrible idea from a rational perspective, though it wouldn't be of much practicality in Florida or other places where the sun shines. I had a good laugh, however, at their naïveté, however. All one needs is a video of some scrote in body armor being shot harmlessly by cops, and the ding-dong thing happens, especially if the scrote is black.
I note that the proposer of the bill is a Democrat from California, which is interesting, because California had a long-standing tradition for the right to bear arms, that is, until the Black Panthers started carrying rifles when patrolling their neighborhoods. There's some powerful imagery there, and it's resulted in a situation where California leads the nation in silly imagery-based gun control.
There are other gun-control traditions, but they make more rational sense: the Sullivan Law in New York started so that police controlled by Sullivan could drop revolvers into the pockets of Sullivan's political opponents as a pretense to arrest them. The situation was such that Sullivan's opponents took to sewing the pockets on their overcoats shut. This is much more obviously the work of rational agents than most things that happen in California.