A better question would be, should Pope Francis consider Trump a Christian at all, since, in the Catechism, it is taught that "extra Ecclesiam nulla salus", or "outside the Church there is no salvation". Just as those who did not board the Ark were not saved. And Church history has been clear that Protestants are not considered Christian because they do not follow the teachings of Christ (in a Catholic point of view, of course).
For example, if the Pope was to call a protestant, who does not eat the flesh and drink the blood of Jesus (in the Eucharist), then how can he call them Christian if Christ said "Unless you eat my body and drink my blood, you will not have life in you." Someone who does not have life in them is not Christian, and not of Christ and are obviously lost.
Aside from doctrinal problems, should the Pope of the Catholic Church (this is the context) criticize anyone's Christianity?
Well, the Pope, as head of the Church, is believed to have been endowed by Christ with the keys to heaven and to bind and unbind ("bind and loose")... well, binding doctrines and laws. So he can exercise the authority to excommunicate people out of the Catholic Church, bu to someone like Trump, who is not inside the Church, it doesn't make much sense. He also has the authority to say someone is not being Christ-like or is a hypocrite, liar etc, if they are openly (which Trump has not been), but anyone has that power. In Catholic teaching, no one can be saved except through the Church, so to comment on Trump's Christianity is actually ignorant of the Pope.
On a side note, why does Pope Francis have a problem with building a wall, only when Trump says it, and not those who also agree one is needed (there already is a wall)? And more importantly, why didn't the Pope have a problem with Obama mocking the Sermon on the Mount, considered to be one of Christ's greatest speeches. I needn't mention the needles war crimes but I'm digressing.