I think it's useful to understand religious intolerance in a few tiers. The following tier-list is a sketch, but I think illustrates the idea:
Tier 1 (most intolerant): Suppress the out-group vigorously, including executions, torture, secret police, interrogations, etc.
Tier 2: Suppress the out-group violently (executions) any time they're noisy, but don't seek them out.
Tier 3: Disfavour the out-group, without permitting conversion.
Tier 4: Disfavour the out-group, permitting them to convert.
Tier 5: Disfavour the out-group socially and informally, but not in matters of enforced law.
Tier 6 (most tolerant): It's illegal to disfavour the out-group.
The reason I mention this is that modern notions of religious tolerance target maximum tolerance (Tier 6 or whatever), but there's a lot of variety through history. For example, I think that persecution of Jews under the Romans was, in some cases, only because the Jews were unwilling to also in-form-only obey the dictates of Roman religion (2nd Commandment makes that tricky). Contrast that with Nazi persecution of Jews, which was much more aggressive about seeking them out. It's worth it to identify that one of those is more tolerant than the other, even if we wish for our society to be more tolerant than either of those.
In that context, my understanding is that the Muslim law of the medieval period is pretty clear about tolerance, and that both Al-Andalus and Baghdad followed these rules. "People of the Book", i.e. non-Muslim monotheists, were granted a large set of very specific protections, while still being treated less well than Muslims. (Note that non-monotheists were not granted protections; I imagine that this did not result in much religious tolerance towards those people, but that's just a cynical guess.) These specific protections were strong enough that it made sense for non-conformist scholars (Christian or Jew, as long as they were monotheist) to migrate from Christendom to Dar al-Islam. Compared to modern west-coast notions of religious tolerance, this isn't great. But it's still remarkable and praiseworthy, especially in contrast with modern Sharia, and in contrast with then-contemporary Christian kingdoms.
In summary: it's not that medieval Muslim states were tolerant by modern humanist standards. It's that they were more tolerant than modern Sharia Muslim states, and more tolerant than medieval Christian states.