Yes, that was the story that was told. It's the same story being told now about the Ukraine war. But that's what it is - a story. The invasion is part of the story, but it's not the whole story and it's not the entirety of the reasons we went to war with Iraq and why we're currently aiding the Ukraine.
And you are seriously suggesting that it is other people who are uninformed about these matters?
Not at all! Like I said, the common story has a kernel of truth, it's not an outright lie, but it's not the whole truth. Some people dig further, others have plenty enough other things going on in their lives to deal with digging deeper. The very same people dig at different rates at different times in their life. For example, I was a kid when Vietnam was going on. Didn't exactly dig deep into what we were doing there and what we were hoping to achieve. To be honest, I didn't dig too deep into the Gulf War or the Iraq War either - at least not at the time.
Gulf War I was about forcing an invader back from the independent nation he had decided to annex, and it enjoyed wide support from the international community. It also exposed a much smaller amount of American troops to potential harm than earlier American wars. There is no reason to expect a person who protested the war in Vietnam to oppose that defense of Kuwait, unless they were opposed to all Western intervention in general. The 2003 invasion of Iraq was a totally different story, and I have seen an increasing amount of online comments that erroneously conflate the two.