This is about all I know on the subject:
Angelina Jolie in blackface
Angelina's Native connection
If Angelina is only a small part Iroquois, she shouldn't call herself Native. And I don't think she has.
I think Angelina's mother was the one calling herself "Iroquois." If Angelina used "Iroquois," she probably was emulating her mother. She may not have understood what it meant or how imprecise it was.
I imagine her mother used "Iroquois" because she didn't know her ancestry more exactly. Which suggests the ancestral connection was weak.
Here's what Wikipedia says about Jolie and her mother:
Life and career
Bertrand married actor Jon Voight on December 12, 1971. The couple had two children: actor James Haven and actress Angelina Jolie. Bertrand and Voight separated in 1976 and filed for divorce in 1978, which was finalized on April 14 1980. In 1978, Bertrand met documentary filmmaker Bill Day (Saviors of the Forest and Missionary Positions, among others). Day and Bertrand lived together for 12 years in Beverly Hills and New York City. Numerous miscarriages ended their hopes of having their own children. As business partners in Woods Road Productions, they developed a film project called Amazonia and sold it to film director Ridley Scott, but the project never took off.
After 1993, Bertrand turned her attention toward producing. She was the executive producer of a documentary Trudell, about Native American activist John Trudell. It was shown at the Sundance Film Festival in 2005.
Could we say Marcheline Bertrand's Native activism inspired Angelina Jolie's humanitarian work? Yes, I think we could.
P.S. You asked about other Native actors. I try to write about anyone who gets a Native role while claiming to be Native. There have been a few cases recently--e.g., Tinsel Korey.