I think the debate regarding gun control is a little beside the point of the thread from what I gather. Obviously that's a contentious issue, and seems to rarely go anywhere useful. Sidestepping that, I think the main thrust of the OP is quite worthwhile in examining: political neutrality in JW parlance is just a way of saying "you're not allowed an opinion." Some cults mandate a strict political ideology that must be followed, but I think the JW method may be perhaps an even stronger form of control. Instead of imposing a political ideology and stating that any ideas contrary to this are bad, they go a step further - they state that any ideas you have on the matter at all are bad.
And our friend here has seen precisely what happens when you express "bad thoughts" to someone in the cult - you're reprimanded and threatened with more study as punishment. Indeed in this case, the study serves two purposes - thought reform (i.e. beat her over the head with the idea that her opinion is worthless) and public shaming (bring her in front of the whole family and make her talk about how she erred). The use of family worship to enforce the cult mentality is also effective because it's typically several people against one outlier, and the outlier experiences extreme social pressure to conform, whereas in a 1 on 1 setting there is significantly less intrinsic pressure.
This is all typical cult control - honest discourse cannot be tolerated. You can only interact in the cult prescribed manner and any deviation will be punished. Honest discourse and exploration of other ideas is tantamount to suggesting that it is possible the cult ideas are not correct. This is a concept that is extremely uncomfortable to the indoctrinated mind and it causes the cult defenses to go up. The cultist switch flips and you're no longer dealing with the person you know but with JWBOT-2000.
All that said, I think it would be a much more profitable approach for you to find an alternative outlet for your views on politics/religion/LGBTQ/etc type topics. Maybe finding another place that you can talk about things and really debate/discuss in an honest manner - this will help you to hold in things that will only cause discord with your parents but it will also allow you to really grow and develop as a person by exploring alternate ideas and opposing views. There's little to no benefit in engaging your parents because they have lots of power to make your life miserable and they are unlikely to fold based on anything you say at this stage.