WASHINGTON — President Trump has railed against undocumented immigrants in recent days, branding many of them “murderers and thieves” who want to “infest our country.” Not long ago, he referred to them as “animals,” although he insisted he meant only those who join a violent gang.

The president’s unpresidential language has become the standard for some on his team. This week his former campaign manager, Corey Lewandowski, made a mocking noise, “womp womp,” when a liberal strategist raised the case of a 10-year-old girl with Down syndrome separated from her parents at the border.

Mr. Trump’s coarse discourse increasingly seems to inspire opponents to respond with vituperative words of their own. Whether it be Robert De Niro’s four-letter condemnation at the Tony Awards or a congressional intern who shouted the same word at Mr. Trump when he visited the Capitol this week, the president has generated so much anger among his foes that some are crossing boundaries that he himself shattered long ago.

The politics of rage that animated Mr. Trump’s political rise now dominate the national conversation, as demonstrated repeatedly during the debate over his “zero tolerance” immigration policy that separated children from parents apprehended at the border.