Well, for one thing, most Muslims don't choose to be Muslims (I recognize there are converts, of course). In the case of, say, Syrian refugees, they didn't choose to be born Muslim in a crappy desert dictatorship that then descended into civil war. Every single gun owner is making a conscious choice to go out and acquire guns.
For another thing, a gun is a valuable physical item that can be transferred from person to person, lost, or stolen. The gun itself can be used to commit crimes, whether or not the original owner still has it. Society has an interest in establishing a registry of who has these dangerous items, just as we have a registry of who owns what car (another valuable object that can be used mainly for good but kills slightly less Americans than guns). A person convicted of certain crimes is supposed to be barred from possessing a gun, but we no way of knowing if that person buys a gun privately, or is given it by a relative. In many states, a person under a domestic violence restraining order is supposed to surrender their guns, but without a registry we have no way of enforcing compliance. A Muslim is not an object, nor is being Muslim transferable or subject to theft, nor is being a Muslim something that you have to give up after being convicted of a felony. I suppose the point of a Muslim registry is to identify people who are thought to be potentially violent; the point of a gun registry is to track the movement and use of an object, not a person.
I understand the perspective of gun owners who don't want to be on "government lists" and I could see how they might consider it to be a violation of their privacy. It is a legitimate concern. However, for good or ill, all of us are subject to various forms of surveillance, monitoring, licensing, etc. etc. to exercise all kinds of rights and privileges in a modern society. I am on a "government list" of lawyers and if I screw up at being a lawyer, I am subject to losing that privilege. Same goes for my license to drive. If you have a hunting license or fishing license, you're on a "government list" that also gives a pretty good indication of whether you have guns. For pete's sake, in most states you have to be on a list of qualified cosmetologists to braid hair for money. Society imposes these kinds of restrictions through a democratic process because we have determined that the infringement on privacy and convenience to individuals choosing to engage in these activities is outweighed by countervailing public policy needs. In my view, choosing to own an object which kills or injures over 100,000 Americans every year is an activity that should be regulated. Large majorities of Americans agree. Our political leadership is supposed to balance these competing concerns and make wise policies, but in this arena as in many others has failed miserably.