I don't understand why you say that white suffragettes didn't want Black women to vote. They did not invite them to things like the Seneca convention but it was the 1800s and no white women were sharing space with Black women as equals at that time. Can you provide some further evidence of your claim, because it seems to quite go against what I've seen — which includes direct quotes from Anthony, who was a Quaker and lifelong believer in social equality.

"In 1866, they (Anthony and Stanton) organized the Eleventh National Women’s Rights Convention, the first since the Civil War began. Unanimously adopting a resolution introduced by Anthony, the convention voted to transform itself into the American Equal Rights Association (AERA), whose purpose was to campaign for the equal rights of all citizens, especially the right of suffrage. The leadership of the new organization included such prominent activists as Lucretia Mott, Lucy Stone, and Frederick Douglass." (source)

"She (Anthony) would not campaign for a federal amendment that enlarged the male electorate and left all women outside the body politic. Speaking to an audience of African-American men in New York City in June 1868, she opined, if voting “be an inalienable right, it is as much the right of the black woman as it is of the white. And you can’t ask it for any class of men, without asking it for all the women who are deprived of it.” That was not an argument that could win over Frederick Douglass. (source)