I think a better offline analogy would be if the president mailed out copies of his official statements a few days after he made them (to the general public), and included a random sample of letters to the editor about the statement. Then one day he starts filtering out letters from those he considers troublemakers.

I'm not sure there's any law requiring him to include anyone's letter; it seems he'd have unlimited discretion on whose letters he wants to bundle. I don't see how 1st Amendment rights would ever require the president to let someone use that venue for speaking.