Since taking office 157 days ago, President Biden has promised to put racial equity at the center of everything he does, pledging in an executive order on Day 1 to take a “systematic approach to embedding fairness in decision-making” as he drafts legislation, hires staff, proposes spending and develops regulations.

But his efforts — which could radically realign the distribution of federal money and benefits in favor of people of color and other underserved communities — are running into legal and political obstacles. They push against limits set by the Supreme Court, which say programs based on race must be “narrowly tailored” to accomplish a “compelling governmental interest.” And they ignite passions at a time when Democrats hold the narrowest majority in Congress and the country is already seething with disagreements about race, power and fairness.

On Wednesday, a federal judge in Florida echoed a court ruling in Wisconsin by ordering a halt to an Agriculture Department program to forgive the debts of Black and other minority farmers after years of discrimination. The judge wrote that Congress must “heed its obligation to do away with governmentally imposed discrimination based on race.”

A small-business program was forced to change its rules last month after challenges by white Americans who say the policy is racist. And around the country, Republicans are promising to tie the president’s equity efforts to a broader culture war during the 2022 midterm elections.

On Capitol Hill, the $1.9 trillion relief package Mr. Biden pushed through in March, known as the American Rescue Plan, included money for health care, child care and poverty programs that disproportionately benefit minority groups, underserved communities and women.

But an emerging bipartisan deal on infrastructure does not include $400 billion for home health aides, a program that benefits many women of color. And it is uncertain whether it will embrace some of Mr. Biden’s other race-conscious proposals.

The challenges to Mr. Biden’s proposals have so far halted only a small fraction of his broader equity agenda, which has already ensured that billions of dollars in government spending have reached African Americans and poor women. Some of the president’s programs, like the child tax credit, are less vulnerable to legal challenges because they are technically race-neutral even as they disproportionately benefit people of color.

But the resistance to Mr. Biden’s pledge to make equity “the business of the whole of government” is an early warning sign of more to come.