In the '90s people were still talking about how Vietnam started off as the Democrat's war. Democrats also tended to be the party that talked about intervention, being the world's policeman.
H.W. and Reagan started plenty of conflicts but the average American saw no impact from these conflicts. They couldn't point to Granada on a map, and Desert Storm was just a fun show on CNN. These conflicts were quickly forgotten and through most of the 90s Republicans were able to position themselves as a party of peace. In 2000, George W Bush's campaign focused on limiting "foreign entanglements" and not acting as the world's police.
It's always been a lie from both parties, but even though it's a lie it's still the kind of message that wins elections.
I've been looking for sources that back me up and I'm starting to think that this impression I have, is less objectively true. I definitely remember in the lead up to the Iraq War, several people reminding me the Republicans had not gotten us into the quagmire of Vietnam or Korea, but rewatching the presidential debates of 2000, it's really hard to find a place where Bush and Gore actually differ on foreign policy.