Here's the thing about all the self-esteem raising propaganda about the great achievments of scientists and thinkers who happened to be Muslim in the past - those achievments themselves rest on the achievments of others, who are rarely acknowledged themselves by the 'Golden Agers'.
So science in the realm of Islamic ruled societies was part of the weft and weave of knowledge as different achievements and civilisations drew on the work of others. In this instance, 'Islamic' mathematics is simply derived from ancient 'Hindu' Indian mathematics. So what? Thats how humans have always progressed.
The issue comes when you elevate and propagandise this for the sake of saying there was an inherent exceptionalism in 'islamic' science and maths and philosophy, whislt simultaneously whitewashing the achievements and influence of 'Polytheist' 'Mushrikeen' 'Hindu' civilisation, the 'Golden Agers' are simply expressing a form of chauvinism themselves, under the veneer of fighting the 'chauvinism' of the evil perfidious West, who have deliberately erased and downplayed achievments by nominally Muslim scientists etc, or achievments made by non Muslims under Islamic dominion.
Ancient Indian mathematics would mean that the lowest of the low, the mushrikeen polytheists, were not in fact jahiliya, but were a sophisticated civilisation that Muslims learnt from. That would skewer alot of foundational beliefs of Islam and central notions of the ummah.
Best keep it quiet then, and keep playing the eternal victimhood card, so even the best of shared human endeavour, science, philosophy, mathematics, that is part of the common human good, the best of human achievments, as civilisations nurtured one another with learning through the osmosis of discovery and knowledge across cultures over time, just becomes another branch of the identity politics (in this case the Ummah Identity Politics) game.
What were the individuals attitude at the time towards knowledge gained from polytheists? Certainly the attitude towards polytheists you discuss above exists today, but I don't think in Islam's "Golden Age" that was the case? These guys drew largely from Greek and Hindu sources, are credit with rediscovering/reintroducing material largely ignored by the rest of the world (if that is the minimum you will allow as their achievement). From what I've read, academic pursuits were available to believing women as wells as non-believers as a whole. My interest lies in that. That society/culture of Islam at that time that was open to ideas from outside of itself (which makes any age "Golden" to me, regardless of actual achievement). What made them shut down? My thought is that whatever happened, it was an internal idea introduced that poisoned the well, rather than some outside impetus.
I do find it ironic that most Muslims look back to this time with envy, yet the inflexible ideas they currently support are the very ones that make regaining the ideas/culture that fueled that time period an impossibility.
Topic: How did stars get their Arabic names?