Rayy Babalola, the founder of the Agile Squad, a project management and consulting firm in Kent, England, was captivated by the responses on LinkedIn but says that it’s not so easy for everyone to drop the labels and forget the struggle and perseverance required to find professional success.

Ms. Babalola, 30, believes that to call herself a Black woman business founder conveys that she has overcome the dual obstacles of sexism and racism. And she feels a responsibility to signal to other Black women that they too can have a path to business ownership.

“Being a Black woman has affected how I have been treated, and that has pushed me to become a founder,” she said. “And you can’t be selfish,” she said. “Just because you found a way doesn’t mean that it’s OK, now you can be silent.”

She thinks identifiers like “female founder” and “Black-owned business” are still important. “Until those terms stop rattling minds,” she said, they need to be used to remind the world that they remain something of a novelty and in the minority.

Nikki Thompson, of Overland Park, Kan., said she never shares her opinion on social media but when she came across Ms. Sumner’s post, she couldn’t stop herself. “Labeling perpetuates the differences we should be seeking to resolve,” she wrote.

As a registered nurse, Ms. Thompson’s responsibilities include continuing education training and paperwork for patients, and many forms ask about race, gender, generational demographics, religion and ethnicity. She understands that data collection is essential when it pertains to diagnosis and treatment of illness. But she questions the value of that data collection in the many other facets of daily life. (Ms. Thompson was happy to answer the question of her age — she will turn 41 next week — but noted that labeling people’s age is part of the problem.)

“What if we drop the labels, maybe the biases would subside,” she said. “This is a daily thing in my career, and I think a lot about words and bias and unconscious bias and how we might decrease it.” (She also said that the pendulum can swing both ways: She has heard relatives say of her male peers, “I had a male nurse and he was very good.”)

Surprised by the reaction to her post, Ms. Sumner acknowledged that many of her experiences are influenced by being a white woman, “with all the privilege that entails,” she said. “But how do I see myself? How do I identify? As a founder, and as someone who starts discussions.”

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