This is the kind of question that really intrigues me. So often in large, complex games like CiV you'll find strategies that seem completely counter-intuitive but end up being superior. The later policies cost so much more than early policies that some quick math shows some interesting things.
To start, it takes 30 SPs to unlock the Utopia Project. With 1 city on all standard settings you need a total of 80,930 culture for this. Let's just assume that you always get the Oracle, so that knocks it down to 72,995 culture required. Now for a Piety game let's say you get into the Classical era in time for your 3rd policy and run straight through, finishing with your 7th policy, popping the free policy from Free Religion on Theocracy and finishing Piety.
If you instead go for Rationalism you'll reach the later techs faster. For example, if you can't get the Sydney Opera House with Piety but by going Rationalism you are able to get it, that cancels out the benefit of Free Religion. And Cristo Redentor compared to the Piety finisher is surprisingly close. If you get CR with 10 policies left to go it saves you 5,130 culture, vs. the 6,450 culture the Piety finisher saves you.
So even though they come so much later, Rationalism and SOH + CR is only maybe 2-3 turns slower than Piety without those wonders. Now that's not counting other sources of extra culture in the Piety tree like Mandate of Heaven, Reformation, or the bonus culture from Free Religion, but I wouldn't be surprised if the faster teching (so earlier museums and broadcast towers) would make up the difference. And that doesn't even consider the other benefits of better tech, like better tiles from Chemistry/Fertilizer/Economics, access to stronger military units if needed, earlier access to non-cultural buildings to aid growth, etc. So oddly enough going Rationalism does seem like a viable strategy for a culture game.