As someone who was, until recently, a history undergraduate, my answer to this is probably a little skewed. But, to lay my cards on the table, I think having a critical and informed understanding of the past is really important on multiple levels, one of which I’ll touch on here.
In political terms, a full understanding of our current political space should necessitate an understanding of the past. For one, this helps us understand how modern our moment is, if that makes sense. Since you mentioned the Republican Party, I think it’s worth bearing in mind that while the modern conservative movement will claim it has roots going back to the founding of the United States, it is undoubtedly a modern phenomenon (for example, an historian like Rick Perlstein would look at the early 1960s, and the rise of Barry Goldwater, as a significant turning point for it).
Another significant point is that understanding and reflecting on a shared history gives you, well, a bullshit detector, to speak frankly. People claim authority by claiming lineage to ancient traditions and immutable values, and being able to understand where its coming from is incredibly important. In your original post, you mention people looking back with rose-tinted glasses views of the past, which aren’t true. If someone thinks that is, they have been either convinced themselves of, or been sold, a false picture of yesterday.
People’s nostalgia and traditionalism should not be reasons to abandon the power of the past. Having an understanding of history can provide inspiration for the present, whether from exemplars or from greater knowledge of what must be overcome. However, it is true that yesterday never returns, and the historical moments of yesterday won’t come 'round again in the same fashion that they did the first time around.