This is a tough question because there has never been a largley athiestic individualist nation. Wether religeous or athiest, collectivist nations still engag in religeous worship, be it gods or state. Their rights depend wholly on the whims of those who interpret their choosen idol of worship's desires. Your right in Stalinistic Russia was to starve for the almighty state, while the ancient Aztec's were blessed with the right to have their hearts cut out and their heads tossed down the steps to the cheering of thousands. All forms of collectivism are insanity. Just differant flavors of it.
The better question would be: "Do you see any differance in the rights held by people in officially Collectivist countries, vs. the rights held by people in countries where Individualism flourishes?"
My answer is, if a people are Individualist, it doesn't matter if they are 100% religeous or 100% athiestic. So long as your right to life, liberty & property are protected by rule of law, both of them would be a paradise of prosperity and human progress. Of the two, I would expect the athiestic nation to have a distinct advantage in scientific progress since Athiests don't believe they already have all the answers. Either would be great and in constant need of vigilance against the ever lurking collectivists.