Some points that are perhaps worth mentioning/adding here:
Unlike Palestine, the Uyghurs are not recognized as a country by anyone; so there's "but they're just separatists we're dealing with" argument.
China deftly oppresses the non-Turkic Muslims (Hui) less, so they can argue it's not all out anti-Muslim stuff they're doing.
Not surprisingly then, the Muslims that have protested the situation in Xinjiang the most seem to be the Turks, at least at the official level. (But Pan-Turkism is also viewed with suspicion by many Arabs, see e.g. (p. vii).)
A good number of Arab countries allied themselves with the USSR for realpolitik reasons, despite the general anti-religious tack of the latter. (Generally speaking, such USSR-aligned leaders/movements, including the PLO, were not hardcore Islamists, but had a more complex ideology, mixing nationalism with some socialist elements, on top of religion.) China is perhaps seen as not much different than the USSR was, overall, in those quarters. The new camps are possibly more worrisome, but the USSR also had gulags, internally deported Muslim minorities (e.g. the Tartars) etc. And, finally, on this point, China actually manages to have better/closer relations with some Arab or Muslim countries that even the USSR didn't have. This includes the Saudi ballistic missile program, built by China. The same goes, to an even greater extent, for Pakistan.
There's not a huge amount of press freedom in the Muslim world, in general. Coupled with the censorship of info at the source (Xinjiang) there's probably not a lot that reaches the average Muslim in re Xinjiang. Call this the double censorship effect, if you like.
Then, there's the means. A police state, even Guantanamo like images/footage, is still less striking than bombs falling on buildings.
Coupled with that, there's the Chinese effort for guided-tours "come and see for yourselves".
And, generally speaking, Muslim countries are not shining beacons of democracy and human rights. So the leaders thereof may not be exactly excited by a discussions of questionable policing practices when they sometimes do that themselves [on a lesser scale] to domestic political opponents, some minorities etc.
Some of those efforts like deradicalization camps in Saudi Arabia, are even praised by the West. So Muslim countries slamming China too much on something that China claims is just that [deradicalization, but] on a grander scale might backfire domestically, too. (Speaking of which, the Saudis give best tours of the latter.)