The syntax seems natural to me, but the phrase "however wide it might be" implies to me that you're not bothered about the cross-section being wide, or even that its being wide is a positive disadvantage, which doesn't fit with the rest of the sentence. If "wide" is supposed to refer to society then it might make more sense, but "wide cross-section" is such a well-known expression that I automatically associate the two.
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PeaceblinkfriendWould 'however narrow it might be' make more sense?