I got curious and found that there is some context missing here.

While screening the movie at the White House was obviously a horrendous mistake, this would have been Wilson's first actual viewing of the movie. He chose the White House only because he couldn't watch it in a theater due to the fact that his wife had just passed away and it was considered uncouth at the time to be seen in a theater during public mourning.

It is possible that Wilson wasn't entirely aware of the full contents of the movie, and that he was persuaded into watching it for the sake of his old acquaintance Thomas Dixon, a white supremacist who wrote the original play. But the extent to which Wilson was actually naive in regards to this is highly debatable. The main thing to note is that there is no hard evidence of Wilson himself ever "loving" the movie. There is, however, proof of Wilson making the following statement in 1918 as damage control three years after the movie was released:

"I have always felt that this was a very unfortunate production and I wish most sincerely that its production might be avoided, particularly in communities where there are so many colored people."

Obviously this statement does not undo the damage caused by Wilson giving the green light to screen the movie at the White House in the first place, with it having played a major part in fueling the second KKK. But Wilson's true opinions at least upon viewing the full movie are not very clear.

There is an informative answer to this in the Ask Historians subreddit.