For example, not just admitting that the idea of race exists but actively pushing boundaries of what we commonly accept it as or searching for the implications in relation to the lives of themselves or others. They are challenging the idea and they're engaging the idea - those are fine but they don't sound quite right. Are there any other words that describe this concept (possibly a noun)?
If someone is struggling with an idea, particularly a moral or ethical one, you might say someone is wrestling with an idea.
Edit: link and definition courtesy of Respect Mah Authoritah
To struggle in trying to manage, control, or deal with something: wrestling with budget cuts; wrestle with one's conscience.
The activity of engaging can be called an intellectual pursuit. The person would be an intellectual.
An intellectual is a person who engages in critical study, thought, and reflection about the reality of society, and proposes solutions for the normative problems of society, and by such discourse in the public sphere gains authority from public opinion.
You could say that the person was ruminating on an idea.
This would mean they were chewing it over and over in their mind, like a cow chewing the cud, (the literal meaning of ruminate) and trying to think carefully about every possible angle to it.
In fact the OED gives the mental process priority of place over the notion of a ruminant chewing partly digested food in the rumen. This is only sense 3 of the verb.
Incorporate!! I was just looking for this word--if it's the word you're looking for that is~
"What does it mean to incorporate something into something? (Entry 1 of 2) transitive verb. 1a : to unite or work into something already existent so as to form an indistinguishable whole. b : to blend or combine thoroughly." https://www.merriam-webster.com/dictionary/incorporate