Separation Of Press and State

The First Amendment is the core of our freedoms:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances

The very first freedom being the free exercise of religion. For this many believe it means the freedom 'from' religion and 'the separation of church and state.' I would think it more appropriate to think of it as a freedom from government interference.

If this line of thinking can be construed in such a way then why not apply it to the other freedoms enumerated? How about the separation of press and state?