I thought even after the merge the Neanderthal genes continued to get rarer, indicating natural selection against them

If it's 2% now after 2000-3000 generations, it must have stabilized because any number <.995 is basically zero when raised to the 2000th power. The neanderthal genes would have to be 1-10^-5 as fit as a the sapiens genes, which is basically noise.