Nobody except moronic, hyper-partisan fuckwads (on "both[1]" "sides[2]") ever argued that the First and Second Amendments were mutually-exclusive, you know!
Personally, even the few hyperpartisan fuckwards I know have never stated anything of the kind. Strawman much?
The problem, that leads many people to contrast the First and the Second Amendments, is not that they contradict each other — no one thinks so — but that we are reading them differently.
The First Amendment is read as liberally and all-encompassing, as the Jews read the prohibition to "cook lamb in the milk of its mother" — combining goat cheese with beef is Treif even though neither are sheep, and a goat can not possibly be the bull's mother. Read like this, the Amendment's right to "petition the government for redress of grievances" is understood as the right to any and all speech — including even production of pornography.
If instead we read the First Amendment the way we are told to interpret the Second, however, only the speech addressed to the government — and only for a redress of grievances — would be a right. Oh, and you'd have to go through a wait-period before opening your mouth. And you'll need a license to exercise that right too.