The word predominate is not a negative word. You might be mixing the word with dominant which could definitely have a negative connotation to it. Dominant applies to something that is uppermost because ruling or controlling. (a dominant social class or person). Predominant applies to something that exerts, often temporarily, the most marked influence. (a predomiant emotion). Predominant usually describes something having the majority but not in totality. In this sentence they describing these people that are "majorily" Muslim. They are not all Muslim. Hope this helps!

It is not a negative word. Consider Syria. We cannot call Syria a "Muslim nation" because, quoting Wikipedia, "Religious groups include Sunnis, Christians, Alawites, Druze, Isma'ilis, Mandeans, Shiites, Salafis, Yazidis, and Jews." However, 87% of the population practices Islam. We could call it a "majority-Muslim nation," but that only means "more than half." Muslims are much more than half. You cannot say everyone in Syria is Muslim, but you can say almost everyone in Syria is Muslim. Syria is "predominantly Muslim." During the election, Trump said "Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what the hell is going on." However, according to U.S. law, a test based on religion would be illegal. As President, Trump has issued several executive orders barring entry to travelers, based on countries, not on religion. Are they an illegal "Muslim ban?" They do not use the word Muslim, they do not bar all Muslims, and there are many predominantly Muslim countries, such as Indonesia, which are not barred. Your quotation is from a statement of opinion by the newspaper. The newspaper is trying to describe the travel ban in a short, yet accurate way. "Muslim ban" would be inaccurate. "Seven Muslim countries' would be inaccurate. "Seven predominantly Muslim countries" is short, accurate, and makes the point that almost all of the travelers affected by the order are Muslims. That much is a fact. This fact is being used to support the newspaper's opinion that the order is actually an illegal, religion-based Muslim ban. The newspaper calls the order cruel, cowardly, bigoted, xenophobic, Islamophobic, spurious, unrighteous, self-defeating. These indeed express a negative value judgement. "Predominantly" does not.

It has a meaning similar to "primarily." the connotation is neutral.

It has a meaning similar to "primarily." the connotation is neutral.

It's not a negative word. It's a neutral word.