Did American involvement in international conflicts with other nations, from 1945 through the early 2000s, lead to consistent patterns or effects in domestic national politics? If so, what were they and why?
If I understand this question correctly, the best answer is that US involvement in international conflicts only led to a consistent pattern or effect after the Vietnam War. Before that, there was not really much of a pattern.
There are two patterns or effects that one might think of in this regard. First, there could have been an impact on presidential popularity ratings when the US entered into an international conflict. There might have been a boost in the polls as people rallied around the president or a drop in the polls as they deplored the new conflict. However, as can be seen in the link below, we do not really see any consistent change in presidential approval ratings when conflicts began. The two Presidents Bush enjoyed a jump in their poll numbers in the Persian Gulf War and the invasion of Iraq, but we do not see anything comparable at, for example, the start of the Korean War or at the time of the Gulf of Tonkin Resolution.
A second effect would be on partisan politics. It could be that the two parties took consistent stands on the issue of international conflict. This is more or less true, but only after the Vietnam War. Since the Vietnam War, the Republican Party has generally been in favor of a more aggressive foreign policy. The GOP believed that the lesson of the Vietnam War was that the US was not aggressive enough in its foreign policy and it resolved to avoid making the same mistake again. By contrast, the Democratic Party believed that the Vietnam experience showed that the US should be more reticent about getting involved in foreign wars. That pattern only emerged after the Vietnam debacle. It was not evident during the Korean War or the beginning of the Vietnam War.
Thus, a consistent pattern did emerge, but only later in the time period that you mention.