As a base case, here is Romney 2012 with 2036 demographics
[source].
As you can see, the future of the Republican Party in presidential elections is not very bright, if they continue to perform as they do now and if demographic changes happen as projected. Of course, no trends last this far out.
Let's mix things up a bit.
Prediction #1: Hispanics start voting a bit more like whites as they assimilate into anglo society. Unlike the base case, this is a map that a Republican candidate can win. That said, Democrats still have a clear advantage.
Prediction #2: Water scarcity becomes a serious problem in the Southwest, a problem which residents experience as skyrocketing utility rates. Eventually, the region's poor are forced to leave, with many of them settling in the Southeast. I simulate that by shifting a percent of Democratic votes from west to east.
Prediction #3: Rising tides and devastating hurricanes cause mass migration from Southern Florida and Southern Louisiana northward, particularly into Georgia. By 2036, Georgia is an incredibly important, elector-rich swing state, the focal point of presidential elections like Ohio today. Both Louisiana and Florida become more Republican. Mississippi tilts over into the D column.
Prediction #4: Northern whites become more conservative. I expect labor force participation of whites, and white men in particular, to continue to shrink over the next two decades. I expect one consequence of this change in the labor market to be white men becoming more susceptible to radical politics, in particularly to Trump-style ultraconservatism.
