Question

What violent incident turned much of the public against the labor movement ?

Answer 1

There are so many in the US it is hard to know which one you mean.
The International Association of Bridge Structural Iron Workers, 1906-1911 was significant.

Explanation:

Union, Anti-Union and Government against Union violence in the USA has a long and bloody history. Union workers often used dynamite to express their displeasure with Employers. In some cases governments have been surprisingly lenient on all sides even when fatalities occur.

International Association of Bridge Structural Iron Workers, 1906-1911, caused violence in a nation wide labor dispute which led to over 100 incidences of dynamite explosions.

The Union and Anti-union divide is a polarizing force in America. Union/Anti-Union violence had calmed by the mid to late 20th Century lessening to mostly fisticuffs between strikers and strikebreakers.

Serious incidences including fatalities still occur.

https://en.wikipedia.org/wiki/Union_violence_in_the_United_States#Overview