You have indeed had racial equality laws for 60 years, but we've had anti-murder laws for 1000 a years and we still get murderers. The question should be whether you have a legal structure in which progress is possible - and in America, until fairly recently, I'd argue that you do. It's slow as fuck... but you moved from the Constitution to a Black President in around 200 years or so. That's progress. It might not feel like it - but by any measure it should be acknowledged as such. You have the framework for the laws to be laid and slowly but surely they have been across multiple injustices and many different groups. I have reservations about running your legal structure around a 200 year old document - but that's my British bias coming into play. It is slow but it is happening - and as I argued with the repeal of Roe vs Wade, the process isn't straightforward. I think it'll be one step back and two steps forward. The repeal, whilst distressing and (to my thinking at least) morally repugnant, was democratically achieved and it'll need to be overturned democratically and overturned for good. I am confident that will happen. I think the moderates will turn blue at the next election.
It is the laws, along with civic planning and broad redistribution of wealth that allows that subconscious bias to erode. Bias is rarely eroded by confrontation, those being confronted often double down. Bias is eroded by general humanity, social mixing and compassion - and both sides, progressive and conservative are moving their bases away from this mindset and fuelling each other. Each base is slowly convincing itself that the world is a far worse place than it has ever been - when, for liberals at least, that is demonstrably not true, and most Conservatives warm to inclusion slowly as and when it intersects with their world.
We must be careful of baking news sets of subconscious bias into the minds of the next generation. If you consider this generation to have begun in 2008 (when Facebook went mainstream) the generation approaching adulthood now have spent most of their formative years never hearing a contradictory opinion, never learning to negotiate and being told by the 'other team' they are evil and by their own team the other guy or girl is evil. We're in danger of sowing the conditions for a civil war and that needs to be addressed as a matter of urgency.
TLDR: you do change hearts and minds with laws, when they're backed up by good social policy. But a) it takes time and b) it must be fair to everyone.