Social issues alone might make Dwight a Republican regardless. We do not know what his views on abortion would have been. Also, someone born in the nineteenth century is rather likely to be a socon.
Eisenhower was definitely a SoCon, but he was very concerned about population growth in the Third World destroying stability and growth potential and illegitimate children in the US being conceived to get welfare benefits. In the 60s he agreed to co-chair Planned Parenthood Federation with Truman. So pro family planning but based on Conservative views and feeling uneasy about abortion, but not outright against it.
With the population explosion increasing (now also affecting the environment) and the under class culture he feared being a lot stronger than back then I think he would have considered abortion a necessary evil. But in general he was way too conservative for the Democrats. Eisenhoewer was a rational and moderate man, but clearly with Conservative core values. But maybe a little too nuanced in his views for the modern GOP.