It's not so much a shift as the US coming into alignment with the rest of the world. Harmful expressions like hate speech and inciting violence have more or less always been recognized as things you don't put up with in a civilized democratic society, just as you don't put up with physical violence to resolve disputes or allowing vehicles to drive any which way on motorway.

The essence of freedom of speech has always been the ability of the common or marginalized folk to discuss and criticize those with power and privilege - the state, the landed, the majority. Attacking marginalized minorities is not the purpose of it and is a categorically different type of action - the marginalized don't have power over others to begin with.

Frustratingly the US is actually rather poor about expression freedom in a number of other ways (ways which ironically almost never come up when Americans talk about speech freedoms), and ranks below many other western nations.