I was responding to your point, "They may have growing populations..." (If you state that, "they may have growing populations" and state here that the "they may have similar and even lower birth rates than the US", then both statements can only be true if they are importing their own Replacement Population as well; otherwise, both statements can't be correct.)
Remember, these predictions are based on “no changes in behavior” for the next 100 years, while a baby boom could ensue at anytime for unforeseen reasons.
A lot of things could ensue at anytime for unforeseen reasons; we can do nothing more than act prudently on the information we have at hand.
Both can be true because their are multiple muslim countries. Qatar and UAE have low birth rates and very high sex ratio imbalance. Those with better sex ratios have higher birth rates.
They are very sick societies.