The suggestion that the UK population is united in any way is fallacious.
The outcomes of the 2014 and 2016 referenda and the 2015 and 2016 parliamentary elections are clear and the majorities are marginal, but majorities they are.
People seem to think that when something major changes, they'll keep all the good things and there will be no drawbacks and they will just gain the new good things.
What will the drawbacks of exiting the EU be?
In starting Brexit, May is taking note of the will of the majority; in planning a second Scottish referendum, Sturgeon is ignoring the will of the majority. Big difference.
After the 2014 referendum the majority went on to vote in 2016 for political parties in favour of Scottish independence... it's not such a big difference.