To my memory, 1993-4 were the critical Clinton years for gun control polarization. It started with the BATFE's "ricebowl" Waco raid, the Ruby Ridge trials during 1993 brought that Republican era atrocity into sharp light, the 1993 Brady Bill passed at the end of the year, followed of course by the 1994 ban on new "assault weapons". Clinton himself credited gun control for the historic loss of the Congress in 1994, and many noted the first re-election defeat of a Speaker of the House since 1862 (when the nation was much, much more polarized, in the middle of a Civil War that killed over 600K).
I don't remember being hardly so concerned in 1996, can't even remember any Federal legislation gaining traction in 1995, although we were very determined to keep the Congress in Republican hands.
I came of political age in the '70s, watched Watergate unfold, can still remember where I was when we learned Nixon resigned; the Left's hatred of him was implacable, I've read that was true since around 1948-50. But things weren't quite so bad after he left the scene. We loathed Slick Willie with a passion (now, not so much...), but we could at times work with him.
The 2000 election, though, that really polarized things, protesting the legitimacy of an election at the highest levels is utterly dangerous (one of the greatest things about our sorts of systems is solving the succession problem, one set of people running the nation replacing another), and Obama hasn't helped.
Although you do have a point about how the MSM treats budget conflicts for a Democratic vs. a Republican Congress. One complicating factor is that the Republicans did not control both houses during the period 1955-1993.
The difference today is other people have audiences. So, instead of becoming the bastions of accuracy and fact checking, the NY Times, ABC, NBC, etc. have continued to be pundits. Washington hasn't changed one bit since the 1800 election, its the fourth estate that tries to influence instead of inform.
Before, when people didn’t have access the way they do now, the small connected elite of politicians and other decisionmakers were able to coerce and smooth out issues for their constituency. Now, for better or worse, the people’s views are being enforced more directly.
As for "access", one counter WRT to this study's claimed time frame is the end of the "Fairness Doctrine", which severely stifled radio and TV political discussion from not all that long after its promulgation in 1949 until its end in 1987 (https://en.wikipedia.org/wiki/Fairness_Doctrine). Conservative talk radio, Rush Limbaugh being the best known example, became a major thing immediately afterwards. That channel, outside the control of the "small connected elite" became a driver of politics well before 1996.
Also I can think of plenty of other causes that are equally or more plausible than the ones cited by the authors:
* MSNBC launched in 1996.
* 1996 presidential election, hotly contested because Democrats wanted to take back the House from the GOP (did not succeed) and Second Amendment advocates were alarmed because of 1993 and 1995 anti-gun legislation. There was the 1996 FBI white house files controversy, Clinton signing the Defense of Marriage Act in 1996, etc.
* Drudge Report launched in 1996 (followed by Lewinsky scandal in 1998).
Though I think greater access to alternative media via the Internet, no matter what your political persuasion, is the most likely cause of greater polarization. You no longer had only ABC|NBC|CBS and your local newspaper and radio station. Republicans now had Drudge, Democrats had MSNBC.com, socialists had wsws.org, libertarians had Cato.org or Reason.com, etc.