For many, it isn't necessarily they are flipping but as the spectrum continually shifts to the Left the DNC moves farther away from them. JFK was something of a folk hero to Democrats, he would be run out of the party now.
And Ronald Reagan would be run out of the RNC on a rail.
Free market capitalism, free speech, individual liberty, limited government are all liberal values and some just see the Right as the side holding up those values.
Progressives are less enamored of maximal free speech than they were a few years ago. However, the idea that the right-wing has become the poster boy for tolerance is slightly amusing.
• There is little indication that they are big fans of minimal restrictions on pornography
• They're still highly critical of artistic freedom
• Conservatives show little tolerance for feminism, LGBT, minority rights, any sort of non-military government program, anyone who is critical of the police in any way, kneeling NFL players, any progressive/civil rights protestors etc
• The rank and file routinely attack and threaten anyone who goes against their values (e.g. social media death threats against feminists are pretty routine)
• To put it mildly, the white supremacist / fascist extreme right wing are only interested in "free speech" for themselves, and have no interest in granting their enemies (or anyone really) free speech rights if they ever gain control
• It should be
screamingly obvious that many Republicans and conservatives right now do not idolize free markets (as shown by attacks on free trade, and happily picking winners in the markets), individual liberty (e.g. antipathy towards LGBT), and limited government (e.g. encouragement of government intervention in social matters, expanding military, expanding law enforcement powers), as well as violating other classic liberal values (e.g. pro-torture, anti-immigrant, anti-voting rights, rule of law (don't get me started), and so on
I.e. intolerance, and forcing groups (in-group or out-group) to toe the line, is not a partisan affectation. The idea that "only libruls object to speech" or "only conservatives object to speech" is myopically self-serving.