It would be good to examine this assumption.

A ripe, and quite fair ground, might be the 2 recent Women's Marches.

- The (leftist) Women's March (for abortion, LGBT rights, etc.)

- The conservative Women's March for Life (against abortion)

Do we see equal amounts of slurs and vitriol at each march? One might examine the signs held by protesters, the videos taken, the violence that occurred.

Study: "Young More Likely to Believe Protest Is Effective"

http://www.pewglobal.org/2014/12/18/many-in-emerging-and-dev...

Study: "Extreme Protest Tactics Reduce Popular Support for Social Movements"

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2911177

You'll likely hear about more vitriolic protests on the left. Again this is mostly influenced by media coverage - protests don't necessarily translate to being representative of whole populations. Protests are largely something young people do (which means more liberal) and the kind of extreme protest tactics that get in the press push more people away than helps - so it's not necessarily drawing wide support, even from within the party.

The media also loves a good protest, regardless if only 100 people show up. Which is again further tilted by media biases.

There's also the generalization that the left is better at organizing while the right quietly shows up in strength at the voting booth. The exception to this rule recently was the Tea Party, which largely took a page out of the left's political handbook and created a visible protest 'movement'. But again that's the exception.

Some people on the right like to joke that people at protests are all unemployed or students, while the conservatives are all adults too busy working or taking care of a family.

So I'm not sure how much you could gather from looking at protests or issue movements. It's possible that young people are just less mature and don't know better than to use slurs and vitriol, which is reflected in group dynamics. Not to mention education and social class.

The March for Life [0] is not now, and never has been, "the Women's March for Life", even in its own organizer's propaganda.

[0] http://marchforlife.org

You would need to account for differences in group size. An equivalent number of slurs out of both would amount to a larger proportion for the smaller group.