Five years ago, as grief and anger over George Floyd’s murder ignited national protests, top Democrats joined the demonstrations, called for cutting police budgets and, in a ham-fisted effort at solidarity, even knelt in kente cloth at the Capitol.

Now, as President Trump spoils for a fight by sending unwanted troops to Los Angeles to stamp out protests and help with immigration raids, Democrats scarred by recent elections have a starkly different message for demonstrators:

Don’t play into his hands.

Five years after the 2020 racial justice movement prompted a wave of cultural changes and then an enduring political backlash, many Democrats are signaling that they now recognize how skillful Republicans can be in using scenes of unrest — whether limited or widespread, accurate or not — to cast liberal lawmakers as tolerant of lawlessness.

“Many of the 2020 protests played out in ways that Democrats did not see and they did not foresee,” said former Senator Doug Jones of Alabama, a Democrat who lost his re-election bid that year. At the time, he said, some did not grasp that “once you got to a certain critical mass of protesters, that some bad things were going to happen.”

“I think they do now,” said Mr. Jones, who stressed that Mr. Trump was needlessly escalating tensions. “I also think that they appreciate the fact that any violence is one, is uncalled-for, it needs to be prosecuted. But it’s also playing into the narrative of Donald Trump.”

So far, the demonstrations now — relatively small, scattered and generally peaceful — bear little resemblance to the mass protests of 2020, which in some cases devolved into destructive riots.