I don't think this is a generational thing. Governments have always been trying to spy on their citizens since governments have existed. Back in the 1700s, John Wallis and the Rossignols were routinely reading diplomatic letters. Before the invention of the internet, the "Special Investigations Unit" of the Post Office was routinely opening people's letters and copying them to MI5. Even Snowden's revelations simply show that the government continues to pry into everyone's private lives - only the scale of the abuse has been magnified.
When so-called "millennials" walk the halls of power, they'll try to spy on their citizens too. Their bogeyman might not be terrorism - that was their parents' bogeyman, and their grandparents' were Communists, their great-grandparents' were Fifth Columnists, etc...
It's not clear how to make the situation any better when both major parties in the UK are committed authoritarians whose security policies are dictated by MI5 and GCHQ. The public, "millennials" or not, in the UK seemed quite unmoved by the Snowden revelations, and seem happy for the panopticon to continue.