The only 'rights' as you refer to are the ones you fight for. The government can't give you rights, but they most certainly can take them away. I think you are confusing privilege with rights, a common mistake.
Here is the real threat here.
If there is no God, then man is just a glorified animal. Man is not a special creation made in the image of God, thus giving man natural rights that the beasts of the field don't have.
But what do we do to animals? Do we not put them in zoos for our amusement, do we not use them as beasts of burden? Do we not kill and eat them? Do we not herd them around on a whim for our own wants and needs, which incidentally that is what socialism is all about.
Charles Darwin once wrote:
“With savages, the weak in body or mind are soon eliminated; and those that survive commonly exhibit a vigorous state of health. We civilised men, on the other hand, do our utmost to check the process of elimination; we build asylums for the imbecile, the maimed, and the sick; we institute poor-laws; and our medical men exert their utmost skill to save the life of every one to the last moment. There is reason to believe that vaccination has preserved thousands, who from a weak constitution would formerly have succumbed to small-pox. Thus the weak members of civilised societies propagate their kind. No one who has attended to the breeding of domestic animals will doubt that this must be highly injurious to the race of man. It is surprising how soon a want of care, or care wrongly directed, leads to the degeneration of a domestic race; but excepting in the case of man himself, hardly any one is so ignorant as to allow his worst animals to breed.
The aid which we feel impelled to give to the helpless is mainly an incidental result of the instinct of sympathy, which was originally acquired as part of the social instincts, but subsequently rendered, in the manner previously indicated, more tender and more widely diffused. Nor could we check our sympathy, if so urged by hard reason, without deterioration in the noblest part of our nature. The surgeon may harden himself whilst performing an operation, for he knows that he is acting for the good of his patient; but if we were intentionally to neglect the weak and helpless, it could only be for a contingent benefit, with a certain and great present evil. Hence we must bear without complaining the undoubtedly bad effects of the weak surviving and propagating their kind; but there appears to be at least one check in steady action, namely the weaker and inferior members of society not marrying so freely as the sound; and this check might be indefinitely increased, though this is more to be hoped for than expected, by the weak in body or mind refraining from marriage.”
― Charles Darwin, The Descent of Man
So, the question begs, what is this "Noble Nature" all about? What is scientific about that? Darwin even uses the term "evil". What is evil in science I wonder? In fact, there is no science to this statement. Noble nature is merely an abstract construct and does not really exist if you ask a scientist, yet this construct is what is supposed to stop mankind from becoming a monster like Charles Darwin warns against here. Instead, someone like Hitler would say that he will take the science of creating a master race like farmers breed cattle to get a genetically superior breed and to hell with the notions of having a noble nature or the existence of evil or the "right to breed". This noble nature is the only thing to stop someone like Hitler from taking genetically flawed patients to the basement of the hospital and disposing of them, never to be seen again, because they drag down society and his precious Third Reich. Unfortunately, that is exactly what happened, and what will happen if people take over your government that don't believe in natural rights.
This is the Achilles heel of atheism and agnosticism and one for which they have no answer.