Were the Grimke sisters right to participate in the abolitionist movement in the way that they did?
Imagine that you are an American living in the 1830's, and you are an abolitionist.
Use specific example from the Grimke sources.
The question you pose also asks for moral and philosophical judgments. Were the Grimke sisters "right" to participate ...
A lot would depend on the criteria used to evaluate what was right. Assuming basic Constitutional principles would apply as a starting point, the Grimke sisters exercised their first amendment right to free speech, free association, and freedom of press. They were nonviolent in their approach.
One might argue that John Brown was not right in that he used violence as a means to achieve political goals, and did so outside the framework of legal government. For the Grimkes there was no similar behavior to judge them and their actions on.
Without knowing which sources you're using, I can't give examples.
However, I would imagine that at least some abolitionists in the 1830s would have been opposed to the Grimke sisters' involvement in their movement. There were two main reasons for this:
1) The sisters were too feminist. It was radical enough to advocate abolition. Advocating for women's rights (and speaking in front of mixed audiences) was more radical yet. This issue was later to split the black rights movement after the Civil War.
2) The sisters were in favor of equal rights for blacks rather than just an end to slavery. This was well beyond what many abolitionists (let alone people like Abraham Lincoln) were willing to consider.