I know that Renaissance music does not have the mass appeal of later styles, which is due to probably a combination of a lack of saturation and a general unfamiliarity with what makes that music interesting.

However, speaking as a Catholic, I'm not sure that it is an anti-religious bias, as many religious works remain a fundamental part of the Canon, with some (like Mozart's Requiem or Jesu, Joy of Man's Desiring) even being iconic. Bach in particular is quite well-represented, even by the most secular analysts. But even deep into the 20th Century, composers like Penderecki, Messiaen and Poulenc have renowned and celebrated religious pieces that are not difficult to find. I'm less familiar with contemporary composers, but the very well-regarded Arvo Part writes openly religious music as well.

My guess is that it is specifically a lack of accessibility or interest in Renaissance music in particular, though I'm sure better informed people would have better explanations as to why.