I am opposed to all active involvement of religion in politics, Christianity not exempt.
That said, there is a meaningful difference. Christianity started as an unrepresented religion of the underclass, so it has a greater capacity for letting the state do its thing without getting involved. Devout Christians can always retreat into leaving the Caesar’s unto Caesar without feeling they are reneging on their religious duty. That doesn’t mean some do not actively try to legislate their moral views, usually with catastrophic results (e.g. south-European fascism in the 20s and 30s). But empirically speaking, countries with majority Christian populations have historically managed to remain secular and democratic.
Islam, on the other hand, is a religion of rulers, conflating the role of secular and religious leadership and ordering the society according to the purported heavenly mandate. Of particular consequence is the concept of Koran as an unalterable, uncreated and eternal manual to life. For starters, what role is there for an elected legislature to play in a system where all the rules are already given? At best, you need a council of religious scholars to properly include airplanes and computers into the preexisting framework. But there is nothing meaningful to be changed about the laws governing family life, personal status, privacy, expression, property, contracts or political structure - unless you wish to deviate from the God-given Law. So what would you want democracy for? Every legislative activity is fundamentally an affront to How Things Should Be.
Consequently no state with a majority Muslim population had managed to maintain the wall of separation in the long term. Not even Turkey with its elaborate deep-state structure aimed at preventing religious influence in political life, resting on Mustafa Kemal’s enormous national prestige. I’m not saying it can’t be done. But the odds certainly don’t seem very good at the moment.