Probably the only place this argument really holds is Iran, because the Iranian revolution was
in some ways a backlash against everything Western due to how the Shah was basically a Western puppet. But even then not really. Qajar Iran had capital punishment for homosexuality. It was only really under the (allegedly bisexual) puppet Shah that it liberalised, to the point of there being a mock gay wedding of two courtiers, Bijan Saffari (painter/architect/theatre impressario who was friends with Empress Farah) and Sohrab Mahvi (designer of the Niavaran Palace) in 1978;



As you may be able to guess from the cartoons, a lot of people were not exactly thrilled about this development and it was specifically used by the Ayatollahs as an example of how decadent the house of Pahlavi had become.
Iraq's Arab Socialist Ba'arth party technically decriminalised homosexuality in the 1960s, but did not approve of it at all and permitted honour killings - and the same "secular commie adjacent leadership" gradually toughened back up on homosexuality going into the 1970s - you can argue that this was the result of the Ba'arths trying to align themselves as Islamic in opposition to the West, but the Syrian Ba'arths never legalised it. The US forced Iraq to make it fully legal again after the 2003 invasion and Iraq's now attempting to make it illegal again.
The mandates introduced laws against homosexuality, but the French mandate specifically criminalised homosexuality under the penal code even though it wasn't illegal in France; this was in response to the religious makeup of the countries it administered. Jordan legalised homosexuality in the 50s (basically copying the homework of the Ottomans for their penal code) but didn't ban honour killings over homosexuality until 2013. The Ex-British protectorate of Bahrain legalised homosexuality in the early 1970s (for similar penal code reasons) but is now trying to ban it again.
And it was basically never legal in any of the peninsular Arab states (Saudi Arabia doesn't even
have a penal code, they just go off Sharia), but that's because they generally follow the Hanbali school of Sunni Islam vs the Levantine population following the Hanafi school; Hanbali holds homosexuality is a capital offence, while Hanafi held that those hadiths were probably not real and so while homosexuality should be punished, it didn't necessarily have a fixed penalty (which is why some legislatures differentiate between it being extra-marital or having caused public scandal).
The cultural acceptance of homosexuality in Arabia is complicated because there was a cultural tradition among the elites for pederasty; Arabic - and Persian- literature contains references to the beauty of "beardless youths" and bemoans how fleeting their existence is (specifically between the onset of puberty but before "the line" of a beard appears - remember they're Arabs/Persians so they get beards young)... but also carries disdain for the khanith/mukhannath (men who shaved their beards in the hopes of still being beguiling to men, sometimes labelled as "third gender"). Which is how you get things like the Bacha Bazi in Afghanistan, which the Taliban had tried to crack down upon while US-backed forces openly practiced it (although arguably the Taliban also secretly practiced it). It's argued these predilection for pederasty so closely mirror the Ancient Greek tradition that they may have been introduced to some regions by Alexander The Great.