Hey,

I can't really talk about earlier medieval times for this, but if you're asking about the conversions of moriscos in the early 16th century you may be interested in this earlier answer I wrote on the topic.

As I mention there, the conversion and later expulsion of moriscos was connected both to Iberian politics and religion - esp. the influence of the zealous archbishop Francisco Jiménez de Cisneros; and to larger geo-politics - with e.g. no more Iberian Muslim states that could oppose the Spanish Crown, and a fear that the moriscos could aid a possible invasion by the Ottomans or other Muslim powers.