Which states do you see moving left or right over the next 20 years and why?

[Kevin]

If the OP is suggesting that the trend with culture wars in this country continues to die down in political importance then I'd agree with what has been said about the following happening.
 
Te development of a more libertarian leaning/socially moderate and mixed GOP comprising
conservative constituencies of  rural voters, wealthy businessman, of varying calibers, religious voters, and conservative leaning moderates, as well as other groups and new recent ones like young highly energetic libertarians, grass-roots activists, conservative leaning policy wonk types and possibly new groups like Asian/Indian voters for example.

As well as a Democratic Party that is overall center-left split between it's traditional working class factions and recent ones like liberal lawyers/academics, and middle/upper income urban whites, therefore appearing awfully like the British Labour Party in nature

The Northeast-The Northeast as a whole moves further to the right on economic issues and some other issues also. The GOP is able to compete and win in places like NJ, CT, ME, and possibly DE again, MD, MA, RI, NY, and VT remain solidly Democratic more or less.

Midwest/Rustbelt-Swing region with the exception of IN. IL, and MN.

Plains- Republican, but things could change in MT, SD, and ND.

South-Still solidly Republican overall except in the case of VA, NC, FL, and maybe WV and TX.

Southwest-Swing region overall, with AZ and NV being swing states while CO and NM lean slightly Democratic. While UT is heavily Republican.

Pacific Coast-CA and HI and to a much lesser extent WA are heavily Democratic, while OR is a swing state and AK is very Republican.

We also have to keep in mind like mentioned above sudden economic resource, or demographic changes which could cause the the political trajectory of states to shift. For example, let's say alot of oil and gas is discovered in MT or SD and over the next 10-15 years alot of people from all over move there aka America's Alberta. Combined with the explosive and diverse population growth, and energy interests who knows what direction this region could go in? Although, admittedly probably Republican like TX has.