It depends on the society and how it's structured. In Western Europe religion is mostly irrelevant today, because a majority of people are non-believers and because morals are not dictated by religion anymore. Although, of course, religion is still very important for some sectors of society.
Obviously, in some nations religion plays a big role and is one of the foundations of society, so it would be very relevant in these. So much so that religion dictates law in some countries.
This answers whether religion is relevant. Another question is whether they should be relevant, which I guess is what you may be really asking, but that is a much more complex question. My inclination would be to let a majority of people decide how to run their society, based on their religion or not, but this may raise other questions like whether minorities are respected, possible external influences and manipulations, etc, so it can't be easily answered with a yes or no.
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