Turns out there is very little empirical evidence showing that stretching prior to or during cycling or many other activities is in any way beneficial.
http://well.blogs.nytimes.com/2011/0...ot-to-stretch/.
The people giving you funny looks know this.
After learning this I took up running again and wish I'd known what bunk stretching was all along. I love running so long as it needn't be preceded by 5 minutes of stretching on the floor.
But really, I wouldn't ever bother to take note of what you describe. I see way weirder stuff going on than people just stretching.