The republican base isn’t conservative in the modern sense, they’re reactionary. In a similar vein, evangelical republicans don’t support the people who embody the values that they profess to hold sacred, they fully, and loudly, back people who are quite the opposite.
I imagine that both groups feel that they’re increasingly losing out in modern society and are seeking someone who’ll crush their perceived enemies and return them to their rightful place ruling the rest of us. So, the allure of a strongman to return them to their imagined golden age.