I actually know a little bit about this topic.
First, you have to look at your premise. You stated "National Parks." The figures for minorities visiting State and Local Parks is significantly higher. The main reason for this is both economical and geographical.
The cold hard reality is that the predominance of racial minorities live in urban areas and National Parks tend to be quite a distance from urban centers. And because of that, getting there, and staying there, can be expensive. And comparatively, whites,on the average, have more discretionary income than racial minorities.
And, as someone else stated, you need to factor in the overall racial make-up of the country. And when you do the numbers move towards the middle a bit.
In the city I live in, which has a population of about 3.5M, there are a great many programs intended to provide access to nature to inner-city youths and organizations. And the reality is that once people are exposed to nature they not only become more connected with something vital to us all but they carry their experience back to their day to day lives. It's proven that when people connect or reconnect to nature they become less apt to litter, more apt to recycle and have an better overall understanding and appreciation for our environment.
But these programs take money. And when certain States are forced to greatly cut back on Park Services, in addition to paying to wage defenses against private entities intent on raping nature for their own capitalistic gains, it's a big hurdle to overcome.
So it's about awareness and access much more than it is about some type of cultural deficiency about what nature can provide.
My advice? Take a hike. As often as possible. Don't litter...pack out what you pack in...find some stillness and connect. (And then spread the word.)