"Because some issues are more important" than our basic civil rights, or some such hogwash."
It is important to understand why people feel the way they do
I absolutely understand why; they're afraid of something in front of them and can look no further. Be it money trouble, personal security, moral threats. The basics. The fears manipulated by tyrants throughout history to maintain a hold over an otherwise uncooperative populace. The party whom the anti-gunners have shacked up with currently hardly has a monopoly on this in America.
Gun rights, as we all know, are rather 'fundamental' at the end of the day, being essentially a baseline indicator of a government's belief its existence is justified/justifiable*, also rather binary at the end of the day, and most importantly not easily reclaimed once lost. Recognizing this requires an educated, logical, long, view; mindful of history and precedent, and wary of unintended consequences or ulterior motives. Healthy skepticism and then some, one might say. Stated intentions of politicians and the present state of affairs play a limited role.
These things require thought, not persuasion or reaction. If a person can't see past their fear of something immediately in front of them, and adopt a strategic viewpoint, there's not much any arguments founded in that perspective can do for them. Yeah, education is possible, but obviously requires both a lot of time for all involved, as well as a rather high level of willingness on the part of the ignorant to expand their understanding --a person motivated by superficial fear is unable.
Our best bet is to prey upon the most contradictory cracks in the rationale for gun laws, and plant seeds of distrust for them as a panacea for society's problems. If possible, conveying onto them an appropriate sense of the betrayal by the people pushing these solutions. That's how I came to realize gun control had nothing at all to do with reducing crime, that the politicians promoting it were uniformly ignorant or outright liars, which led to the realization that without a crime-reduction purpose or effect, there was no reason for the laws to exist at all, other than to function as selectively-enforced punishment tools for authority figures (with the added benefit of theoretically insulating them from unrest, though I dispute the practical effect of gun control to this end)
In the end, they have to
choose to hear our arguments, then
think about whether their understanding needs additional information to resolve contradictions, and
seek that which is necessary to do so. I did, initially because I believed it important I know how to operate and shoot a firearm (Boy Scouts background, no doubt). Someone with no such inclination would shut down the very first time they were contradicted.
We all know darn well we evangelical gun owners play but a small part in directing any of those steps of evolution, and are mostly useful as an available resource & good example.
TCB
*One could also argue gun rights measure some combination of; the rule of just law, individual liberty in general, and the consent of the governed granted to the government --which are themselves something of a three-legged stool, each crucial to each other and necessary for a healthy human society