Earlier quoted context omitted.
I don't follow your example. If the religious vote according to their genuine preferences, they would pick their brand of theocracy as the first option and the secular option as the second. IRV would then eliminate two theocracies in the first round and then secularism would win by a landslide in the instant run-off. Yes, there are games which can be played that increase the chances of some minority group in the seco…
> FPTP election [...] pretty much guarantees theocracy in your example Yes, FPTP doesn't fare better here mechanically. The advantage of FPTP (which, to be clear, I still think is terrible) is that most voters understand that they need to vote strategically and understand how to do that. IRV is often sold on removing the need to vote strategically, and it does not do that, while making the correct strategic choice mo…
The IRV case here is simply a cheaper way to organize a delayed runoff; voters are usually adept at understanding the implications of strategic voting, as long as it's framed correctly: in case your preferred option does not make it to the second round, would you still go to vote, and which would be your other choice? In Europe there is a long tradition for the two round delayed runoff, but it's certainly not presented to the voters as "you can chose anybody in the order of preference and it will be magically solved by the system".
Two round is in almost any case superior to FPTP, so if you can get it by simply tweaking the ballot paper and allowing second and third choices (IRV), it's an easy upgrade.
Approval voting might be closer to a Condorcet winner in some cases, but it's not a panacea to center squeeze because it's vulnerable to honest voting. What we see in practice is a tendency to function as FPTP, as all sides have an incentive to demonize the center and train their voters to mark a single option. So, in your example, the Sunni or Shia Muslims which can't stand themselves enough to approve each other but would still prefer islam in the second round (if secularism is not available), would lose the approval vote to a well disciplined contigent of Buddhists.
IRV solves that by not providing any help to competitors in the first round, and moving the "lesser evil" decision into the second round, encouraging more honest voting. Short of some Condorcet method (which will never be practical or intelligible by the average voter), IRV is an "acceptable compromise".