Like the title says, from John Wayne to Band of Brothers, I have almost never seen a soldier wearing his chinstrap. Is this another case of movie magic obscuring reality or was this actually factual and, if so, why did they choose not to wear them?
Good question, the simple answer is that while a helmet won't directly protect from a bullet or shell fragment, they did protect from glancing shots and ricochets, the velocity of the bullet/fragments being mostly spent by the time they impact the helmet. That said and especially in the case of shell fragments, the force with which they strike the helmet can jerk the head back. A fastened chin strap then has the potential to strangle and possibly damage the neck of the soldier. Experience soon led soldiers to keep their chin straps unbuckled to avoid this, a shell fragment might strike and knock the helmet off but won't result in an injured neck.
Source: Soldiers during the First World War did the same thing with the chin strap often worn buckled behind the head
Jonathan King - The Western Front Diaries: Winning World War I
Helmet straps are a curious topic around here. There's lots of room for more discussion on this, but you can get started on a few previous posts
How were uniforms modified by soldiers? - this one links to an interesting little survey of some WWII photos, where they found chinstraps correctly fastened only 6% of the time
"don't button your chin strap" - David Kenyon Webster (WW2) - Why did he say this? - an unfastened helmet won't strangle you
Why do American soldiers in WW2 not use their helmet straps? - a few more considerations
Leather strap on WWII helmets? - or maybe you're thinking of the liner strap?
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