I think this is basically true. although there are some issues that are so polarizing that they take precedence over the false positive vs false negative preference. the examples that immediately come to mind involve enforcement and punishment. the right generally seems to accept policies like stop-and-frisk or demanding ID from brown people near the border, regardless of how many of those targeted turn out to be doing nothing wrong. the left pretty much takes the same position on campus sexual assault cases, although it at least asserts that false positives are very rare.
False positive and false negative rates also have a relation to the injustice of a false positive. Having to provide ID and get frisked sucks but being falsely accused of a crime and having your entirely life destroyed even if rare is a massive injustice. This is the entire premise of Blackstone's Ratio
Yeah, I think false-positive and false-negative aren't exactly the right construct to consider for some scenarios. It's more like "whose suffering bothers you more?" People in need or those whose contribution is wasted? The racially-profiled or those who may be harmed by criminals if we aren't diligent? Wrongly-accused rapists or rape victims?