First, everyone loves Creedence and their music crosses the political spectrum big time. Fogerty might be a liberal Democrat but his music hits big with conservatives. This is where the more conservative approach in lyric writing the article points out works in their favor. CCR never really wrote a drug song except for maybe "Lookin Out My Back Door" and that is hardly explicit. "Fortunate Son" isn't anti-war by being against the war, its anti-war by pointing out the injustice of the elite, the powerful, and the decision makers of America not having to put their own children on the line and deal with the consequences of their decision to go to war with Vietnam. The love for CCR is so widespread that Donald Trump used "Fortunate Son" in a campaign rally, unaware of the irony considering he got out of the draft.
Second, most of their songs are pretty easy to pick up and play. And because of the first point, they're all crowd pleasers. I'm in my mid-20s and when I picked up the guitar some of the first songs I learned once I got my chords down were "Have You Ever Seen The Rain" and "Bad Moon Rising". Why? Because everyone knows those songs and my dad get a kick out of it.
Maybe Creedence Clearwater Revival will never hit the philosophical or virtuoso depths of some of its contemporaries, but there is enough substance there to not just be a generic commercial pop song. Yet they are simple and universal enough to enmesh themselves into our American culture.