I think imposing secularism on an overwhelmingly Muslim country was overreach by western-influenced elites. But nonetheless, Bangladesh’s Constitution, which was legitimately adopted by a government that had the support of the people, expressly incorporates a principle of “secularism” (using those words). Article I of the French Constitution likewise states that France is a secular republic: “La France est une République indivisible, laïque, démocratique et sociale.” Secularism in France, too, was legitimately adopted into law by elected governments.
By contrast, the US Constitution doesn’t mention secularism or anything like it. It has a prohibition on the federal government interfering with established state churches, and a protection of freedom of religion. In that respect, the First Amendment is more comparable to the German Basic Law, which guarantees freedom of religion but lacks any requirement of secularism. And the Basic Law has been understood to allow quite a bit of public religion. Religion classes are required in school (though you can opt out and take a class in secular morality instead). Government buildings in Bavaria are required to display crosses. There is a church tax. I think the German approach better fits America both as a legal matter and in terms of what the people want. (America is by far the most religious developed country—the percentage of Americans who pray daily is comparable to Iran!)
What happened with the Establishment Clause in the US is more like what Ershad did in Bangladesh: he changed the constitution from its original meaning, without going through the proper means for amending the constitution. At least in Ershad’s case, the public probably supported theu result. Even as of 2013, most Americans still opposed the prohibition on school prayer.