Doing a ritual does something within our mind and our will, it affects energy, and in many cases it communicates with and invokes the aid of certain spirits. The first time that ritual is done, all of these things are shaped a certain way for the first time. As it's done over and over in the same way, it builds a pattern--in our minds, in our will, in the energy, perhaps in the collective unconscious.
The spirits who work with us recognize the ritual and know what we intend to do. All these things together are sometimes thought of as a container--like the clay pot, or maybe like a clay tube that power flows through--doing the ritual a certain way gives the container a certain shape, and the container shapes the power and directs it in a certain way.
When a ritual is done that way, over and over, for years or centuries, the container becomes very strong, and the ritual can have tremendous power. But when someone does the ritual not in a good way--without understanding, without the internal shaping that goes on in the mind and heart, without connection to the same spirits, without getting parts of it right, or doing it in the wrong season, or in the wrong way--anything that takes it out of its context and pattern--then it weakens the container.
The idea is that the container acts a little bit like you do when you learn how to do something so well that it's automatic--then you start doing it a different way. You won't do it as well. Even when you go back to doing it the first way, you still won't do it as well.
Now, what if the thing you learned to do was to control huge amounts of power? If you suddenly didn't do it as well, there are lots of possible outcomes. You could just be less effective at doing what you meant to do. Another outcome is that you could fail to do what you meant to do, but the energy could ricochet off somewhere and do something you didn't intend for it to do. Or you could get hurt.
The non-Native person could be fine, and whomever they did the ritual for could get hurt. The energy could also go off in some unknown direction and hurt someone or something without the non-Native person even knowing it happened.
Or a Native person could do the ritual, and the weakened container could cause them to be less effective. It could harm them or cause them to get sick.
When Native people get angry about non-Native people using Native rituals, sometimes it's about oppression and cultural identity. But sometimes it's because they see dangers that those outside their culture cannot even imagine. And they see potential losses that are incomprehensible to outsiders.
Some of those containers have been shaped for centuries. If weakened or broken, they would take centuries to replace. And some of them are important in ways outsiders can't conceive. Some Native people see potential damage not only to their own families and tribes--but also potential damage to the ecology. In some cases, severe damage. Native people don't just do rituals for their own personal connections to nature, or for healing their friends--many of them do work that helps sustain the land, the plants, the animals...the earth herself.
You may disagree with them, and you may wish they wouldn't get so angry; but try to understand what they believe is being threatened when people not rooted in the culture use the culture's rituals. It's not about race.
Let me say that again:
It's not about race. It's about being rooted in the culture. Many of these rituals simply cannot be done correctly unless you grew up in the culture, speaking the language. Others can be done by kindred spirits who immerse themselves in the culture. Some can safely be done by openhearted visitors. Only those in the culture can tell you which rituals they consider safe to be done by outsiders. It's not about race. It's about culture. And safety. And keeping the rituals powerful enough to do the work they are needed to do.
This is as close as I can come to putting into words the elementary levels of understanding I have around this. May this help bring understanding.
Bright blessings on your path.