Technically there was not solely a queue requirement: the important part wasn't so much the queue as the requirement that forehead hair be shaven – it's just that you tied what was left into a queue, if there was indeed anything left. Buddhist monks, for example, were allowed to shave their hair fully, and certainly some old Ming loyalists such as Lü Liuliang opted to do the same instead of wear the queue. Even during the Taiping War the queue was actually worn by both sides – the 'Long Hair' (changmao 長毛) worn by the Taiping was that on their unshaven foreheads. Importantly, insurrection was always an immediate threat, be it religious or secular, and the queue served as an easy way of marking out loyal vs. disloyal elements – it is perhaps no coincidence that many revolts (most notably the 1796-1804 White Lotus and 1812-13 Eight Trigrams revolts) were sparked by Buddhist extremism.

Sources:

• Tobie Meyer-Fong, What Remains: Coming to Terms with Civil War in Nineteenth Century China (2013)
• Jonathan Spence, Treason by the Book (2001)