Here is the paragraph from the transcript (https://www.whitehouse.gov/briefings-statements/remarks-pres...)

> There will be exemptions for Americans who have undergone appropriate screenings, and these prohibitions will not only apply to the tremendous amount of trade and cargo, but various other things as we get approval. Anything coming from Europe to the United States is what we are discussing. These restrictions will also not apply to the United Kingdom.

It reads a whole lot cleaner, i.e. like you would expect from a speech, if the statement about cargo was intended to say it was not prohibited.

My best guess is honestly that it was meant to be "these prohibitions will not apply to the" instead of "these prohibitions will not only apply to the". Inserting an extra "only" is a pretty easy mistake to make when reading text out loud.