He wouldn't have. Ike had a genepool Plains-German dislike and distrust of the Democratic Party; the only reason he was seen as a potential Democratic substitute candidate in 1948 was that this was not commonly known at the time. I don't agree with the idea that he wouldn't have any issue with Bush or with Trump at all, but I think he would chart a course much closer to someone like Romney or Liz Cheney than to the Lincoln Project if he were alive and politically relevant today.
Yea, I agree with this analysis, though it is hard to say just how some historical figure would react in a future environment. One thing I have been pressing back hard against lately is the underestimating of political divisions in periods of "political consensus". These always come across as down playing the divides that rose up to fill the vacuum or a generally dismissive stance towards a previous policy position because such is not well regarded by the mainstream today.
Just because a lot of Republicans were of moderate temperament and "accepting of the New Deal", doesn't mean that every Republican could have just have easily been a Democrat.