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Originally, they stipulated immigration only from white Europeans. It wasn't until the jews came over late 19th century they pushed diversity. It was the poet Emma Lazarus who added the 'give me your poor' etc to the statue of liberty.

They didn't leave a loophole.

If you read pamphlets on the Constitution which was the written stuff distributed to states to try to get them to ratify the new constitution at the time the Constitution had been written in Philadelphia to move us toward a more federal government from the loose confederation of states you'll see that to them it was so preposterous that people in the United States would ever allow muhammadin's which is what they called Muslims and others into the country that they didn't think it was necessary to specifically exclude them. No Jews signed the constitution. Only one Catholic sign at the constitution. The whole country was Protestant Christian people. Only landowners could vote. They didn't leave any loopholes what happened was the words got redefined about who was acceptable.

In one of George Washington's final speeches he said we have left you with a country full of people with common beliefs and how important it was to keep that. Their intention was clear.

https://archive.org/details/pamphletsoncons00fordgoog

I imagine it'd be of poorer quality though. That sounds plausible