Mustafa Akyol's Tech Central Station column
explains succinctly that the two are indeed compatible.
That doesn't mean that the governments
of Islamic-majority nations are compatible with capitalism. The Index of Economic Freedom shows that the "mostly unfree" Muslim nations have a modest lead over the "mostly free" nations, that none are in the "free" category, and that three (Turkmenistan, Libya, Iran) are "repressed."
Interestingly, with the exception of Jordan
all the "mostly free" Muslim countries border the Persian Gulf: Bahrain
, Saudi Arabia
, United Arab Emirates
. The only other Gulf states besides Iraq (which is currently unrated) and Iran are Oman
, both of which are within striking distance of "mostly free" status. Only Bahrain is in the upper half of that category (2.01-3.00) with a score of 2.23.
These nations tend to score worst in the subcategory of government intervention, in part due to nationalization of the oil industry - big surprise. Barriers to foreign investment are especially high in Saudi Arabia, UAE, and Qatar.