Disclaimer: This is not a perfect comparison but it is a workable one. It's traditional at this point to say something like: “I'm not a racist for talking about Islamic terrorism” but I doubt that will hold any weight for anyone wanting to call me a racist for talking about Islamic terrorism.
The American Gun Control problem can be phrased simply as: “Is the gun owner a good gun owner or a bad gun owner?” The bad gun owner is the angry teenage boy who will go into a school and shoot people. The good gun owner is the woman wanting to make sure she can defend herself, if assaulted. The difficultly is twofold: a) determining which is which at point of purchase and b) determining which is which within the gun owning community (36% of US population).
The Islamic terrorism problem can be phrased similarly: “Is the Muslim a good one or a bad one?” The bad ones are the angry men who will drive cars into people and blow up pop concerts. The good ones are happy to co-exist with Westerners. The difficult here is also twofold: a) determining which is which at point of entry into the country and b) determining which is which within the current Muslim community (4.5% of UK population).
In both cases, a minority of each community are violent killers who will show no regard for the sanctity of human life. The very existence of this minority brings the whole community into disrepute.
In both cases, there is also, I think, an element of the ideology (Gun Ownership and Islam) which lends itself to distortion and violence. This is of no surprise, as human nature is such that any ideology can and will be corrupted. Arguments can be had on the relative ease in which these two ideologies can be channeled into violence but regardless, both have their violent minorities.
Enough about the problem, what is the solution? There is no easy answer as there is no easy way to determine the intentions of the human heart. Good and bad gun owners can look exactly the same, so can good and bad Muslims.
One solution to to always assume the worst and argue that no one can be trusted to own a gun and no Muslim can be trusted not to turn violent. The Alt-Right would favour the latter, arguing for a forcible return to 1920s demographics. The Anti-Gun lobby would argue similarly for a complete ban on gun ownership. Interesting, those who argue for a complete ban on gun ownership are likely to argue strongly against any kind of Muslim ban, while logically both positions are similar responses to similar problems.
In both cases, the extreme solution is unworkable. With the Muslim ban in particular, to target one group of people would be immoral and go against the basic freedoms in the West to practise religious belief. The community of gun owners in the USA and the community of Muslims in the UK are both too firmly entrenched to ban or remove. In fact, attempting to remove them would only grow the violent minority through the narrative of victim culture.
The other extreme is to simply accept that the violent actions of the minority are the price for allowing the community as a whole to exist. This solution must be reinforced after every attack. School shootings have nothing to do with gun ownership and Islamic terrorism has nothing to do with Islam are common platitudes, repeated endlessly every time people are killed. This approach may last for a while but the patience of society is limited and at some point the desire to action will overcome the pressure for inaction. It is also based on a lie, the truth is that logically, if there were no guns in the US there would be no School shootings and if there was no Muslims in the UK there would be no Islamic terrorism.
Is there a middle ground between the two solutions? I propose there is. Going to the science of economics, we find a principle called “signalling”. This is an action a person will take to signal something about their characteristics. University degrees are a signal (but not a guarantee) of intelligence.
For the gun ownership and Islamic terrorism debate, we need to identify the signals of the violent minorities. This would then allow pre-emptive action. However, going down this route involves two compromises. The first is that innocent individuals will be implicated by sending out false signals. The second is that the liberties of the signalling group will have to be extremely curtailed.
To give a hard example: travelling to certain countries could signal that a person is in the violent minority. They are therefore prevented from returning to their home country. This will impact the innocent and the guilty but it will not impact the whole community. Hardly an ideal state of affairs but better than the alternative (people dead on the streets).
To conclude, doing nothing and banning everything are terrible solutions to the problem of Gun Ownership and Islamic terrorism. What is needed is an approach that focuses on identifying the signals of being part of the violent minority, taking strong action against the signal group and reluctantly accepting that the innocent will be wrongly punished in the process. It's not an ideal solution but I've yet to come across a better one.