Probably not. The Supreme Court has held consistently, for more than a century, that constitutional protections that normally benefit Americans and people on American territory do not apply when Congress decides who to admit and who to exclude as immigrants or other entrants. This is called the plenary power doctrine. The Court has repeatedly turned away challenges to immigration statutes and executive actions on grounds that they discriminate on the basis of race, national origin, and political belief, and that they deprive foreign nationals of due process protections. While the Court has not ruled on religious discrimination, it has also never given the slightest indication that religion would be exempt from the general rule.
There is even precedent for Trump’s plan. In 1891, Congress passed a statute that made inadmissable people who practice polygamy (directed, at the time, at Mormons), and in 1907 extended this ban to people who “who admit their belief in the practice of polygamy.” While Congress later repealed the latter provision (the former seems to be still on the books), no court–as far I know–ruled it unconstitutional.
The plenary power doctrine is universally loathed by scholars and some have argued that it is effectively a dead letter. But any honest answer to a journalist’s question about whether Trump’s plan to ban Muslim immigration is unconstitutional should start with the plenary powers doctrine, and observe that it would be an uphill battle to persuade the Supreme Court to abandon a century of precedent. Unfortunately, that is not what scholars–who certainly know better–are telling journalists. They are likely being abetted by journalists and headline writers who don’t like the idea that Trump’s ban would be lawful. Not everything that is stupid or offensive is unconstitutional.
(N.B.: blocking American Muslims overseas from entering the country would certainly be unconstitutional, and blocking immigration by Muslims would raise complicated international-law questions.)