I've not followed the current Trump v Media war close enough this week to profess to know exactly where each side stands at present. But I think the media needs to get over its self indulgent First Amendment games. Yes, First Amendment guarentees a free press. But it's not an endorsement any present media outlet or its present day practices.
As for anonymous sourcing, I don't know what rules, if any, guide today's media. Meida used to be very cautious about such things, but a bunch of the stuff that flies today as "mainstream media reporting" would likely have never gotten past editors if media had half the internal checks and balances it had a decade or two ago.
As for media whinning that some were excluded from a White House press briefing, get over it. The First Amendment guarentees a free press. Go ahead and read it for yourself. Nowhere does the First Amendment guarentee White House access.