Over his decades in the public eye, former President Donald J. Trump has a well-established history of making degrading and racist remarks about women, people of color and pretty much anyone else who crosses his path.

It is a proclivity that dates to his days as a reality television star and that has only expanded in the meme-driven era of social media. In the words of Senator Kevin Cramer, Republican of North Dakota, Mr. Trump is “an equal opportunity offender.”

But in Vice President Kamala Harris, Mr. Trump has found a particularly complicated and risky target for his trademark brand of transgression, as more Americans are suddenly tuning in to what has become a highly competitive race.

Although there are no clear signs that Mr. Trump has increased the quantity of abuse he levels at his opponents, his decision to repost a string of sexually and racially charged broadsides in recent weeks suggests that he has turned up the dial when it comes to pure vulgarity and crudeness.

That eagerness to offend is likely to receive increased scrutiny as the election enters its final stretch. With both major parties battling for female and moderate swing-state voters, Mr. Trump could potentially alienate an undecided audience uncomfortable with his coarse rhetoric.

Since July 21, when President Biden stepped out of the race and endorsed Ms. Harris, Mr. Trump has directed a seemingly constant fusillade of invective at a challenger who happens to be Black, South Asian and female.