As millions of Americans protested at “No Kings” rallies across the country, onlookers gathered in Washington on the president’s birthday for a muted celebration.

Palantir, the data analysis and technology firm whose contracts with the federal government are expanding, and Coinbase, a cryptocurrency firm that donated to the president’s inauguration, also sponsored the event. Oracle, a database company whose co-founder is a close friend of Mr. Trump’s, received a shout-out on Saturday as a sponsor.