Final answer:
The given statement is true.
Step-by-step explanation:
The statement that men in the U.S have become more Republican since the 1960s can be verified using multiple sources. According to studies, the Republican Party has moved further away from the political center compared to the Democratic Party, which suggests a more conservative shift.
Additionally, there has been a widening gender gap in voting preferences, with women tending to lean more towards the Democratic Party. However, it's important to note that individual voting preferences can vary and not all men in the U.S. identify as Republican.