There really isn't going to be one answer because there is a massive difference between forcing someone to switch branches of the same religion (catholic to protestant for example) and time in history.

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For the most part an uneducated peasant really isn't going to be hard to 'convince' to convert because most religious rules are pretty similar. Oh God is called Allah now, but realistically not a whole lot is changing there. Or now the big holy day/time is Saturday evening instead of Sunday morning. Really minus religion specific things (like genital mutilation) that guy whose farming really isn't going to care all that much

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Really the 'hard sell' is the nobility and other influential figures. Don't think of Christianity vs Islam (or whatever) as two competing religions - they are two different 'lords' that don't like each other. Generations of fealty to the first lord is important because that lord likely knows your family and may even have family members working for them and the lord won't want those family members associating with you anymore because of the concern that they will also defect. Maybe some/all of your family's property is contractually bound to the first lord and if you defect you lose everything.

This is one side of the scale, the other is the guy who currently has a knife to your throat is telling you to join his lord and if you don't he is going to kill you. It probably isn't all that shocking to realize that many people are more interested in not having their neck sliced open than they are keeping the first lord from becoming upset.