Hard-right House Republicans are pushing to use the yearly bill that sets the United States military budget and policy as an opportunity to pick fights with the Biden administration over abortion, race and transgender issues, imperiling its passage and the decades-old bipartisan consensus in Congress around backing the Pentagon.

Republican leaders have scheduled votes beginning on Wednesday on the $886 billion measure, but as of Tuesday evening, they had yet to dissuade their ultraconservative colleagues from efforts to load it up with politically charged provisions to combat what the G.O.P. calls “wokeness” in the military.

Those proposals — including rolling back a Pentagon policy providing service members access to abortions and defunding the military’s diversity, equity and inclusion programs — would alienate the moderate Republicans and Democrats whose votes would be needed to get the bill through the narrowly divided House.

The situation has turned the annual defense policy bill into the latest test of Speaker Kevin McCarthy’s leadership since the far right revolted over the debt ceiling deal he forged with President Biden, grinding the House to a halt to demand more influence over its agenda. Right-wing lawmakers have threatened to do so again if their priorities are not met, and this time, their tactics could ensnare what is widely seen as one of the few must-pass pieces of legislation before Congress each year, normally drawing broad support across the political spectrum.

This year’s bill would grant a 5.2 percent raise to military personnel, counter aggressive moves by China and Russia, and establish a special inspector general to oversee U.S. aid to Ukraine. But the legislation has in recent years increasingly become a magnet for cultural fights, and with Republicans now controlling the House, right-wing members have attempted to exploit it to power their socially conservative agenda.

At issue is a major piece of the Republican Party’s attack on Mr. Biden and Democrats, whom they accuse of trying to infuse radically liberal policies into all areas of American life. The Pentagon has figured prominently in their narrative, because it allows Republicans to tie their complaints about cultural issues to national security and patriotism, effectively arguing that progressive policies are not just misguided but dangerous.

“I believe that it is core and fundamental to defense that we stop making the Defense Department a social engineering experiment wrapped in a uniform,” Representative Chip Roy, Republican of Texas, said in an interview.

Mr. Roy said he eschewed ultimatums but would “expect” votes on rolling back Pentagon policies regarding abortion and diversity, signaling he otherwise would not support allowing the bill to reach the floor.

Conservatives have also proposed several provisions targeting transgender troops, including one that would deny coverage for transition services and another that would force them to use facilities that correspond to their sex at birth.

Republicans have already inserted some provisions into the bill that appear intended to stoke culture-war debates. During a drafting session last month in the House Armed Services Committee, G.O.P. lawmakers added bans on drag shows on military bases and instruction on critical race theory.

But leaders in the party fear that conservatives’ demands for even more social policy dictates could rupture the bipartisan coalition they have built around the bill, which received near-unanimous approval by the armed services panel.

“We had a full, healthy debate, a series of debates,” Representative Mike D. Rogers, the chairman of the armed services panel, said on Tuesday during a Rules Committee hearing, referring to the drafting session last month. “There were several amendments that were adopted to deal with this.”

Mr. McCarthy’s small majority means he can afford to lose no more than four Republicans on any vote, giving factions of his party outsize leverage to make demands. Last month, 11 hard-right Republicans, including Mr. Roy, managed to bring the House floor to a standstill by withholding their votes for a rule governing legislative debate, in protest of the debt ceiling deal.

It was not clear whether those lawmakers or others might do the same thing with the ground rules for the defense bill, which would block it from being considered.

“I’m voting for the rule, and I’m voting for the bill,” Representative Matt Gaetz, Republican of Florida, said in an interview, after promising that conservative Republicans would force votes to “reverse course on the radical gender ideology at D.O.D.” Mr. Gaetz was one of the lawmakers who protested the debt ceiling deal by holding up other action on the House floor.

Republicans are unlikely to get any assistance from Democrats in bringing the defense bill to the floor if the measure caters to conservatives’ demands, and could lose critical Democratic support needed to pass the legislation if Republicans vote as a bloc to roll back the Pentagon’s policies on race, gender and abortion. In any case, party-line passage of the bill would be virtually unheard-of on Capitol Hill, signaling the erosion of a rare pillar of bipartisanship in Congress.

Democrats argued that rolling back diversity initiatives at the Pentagon would be compromising the military’s future.

“A diverse force is crucial,” Representative Adam Smith of Washington, the top Democrat on the Armed Services Committee, said on Tuesday before the Rules Committee, pleading with lawmakers not to allow a vote on the proposal. “We have recruitment challenges. We cannot take large groups of people and exclude them from that process. This is about national security. This isn’t about a left-wing political agenda.”

They also expressed no confidence that House Republican leaders would succeed in bringing conservatives to heel.

“It looks like the Freedom Caucus is telling them that ‘We can’t move forward unless we get our way on some of these divisive issues,’” Representative Jim McGovern of Massachusetts, the top Democrat on the Rules Committee, said in an interview on Tuesday. “And if history is any indicator, when the Freedom Caucus says, ‘Jump,’ Kevin McCarthy responds by saying, ‘How high?’”

Should Republicans succeed in shepherding the bill to the floor, mainstream Republicans could help defeat some of the conservative social policy proposals.

Representatives Don Bacon of Nebraska and Michael R. Turner of Ohio, both Republicans, refused last month to support the proposal to eliminate funding for the Pentagon’s diversity, equity and inclusion programs.

“To say you’re going to fully defund diversity training, that doesn’t make sense,” Mr. Bacon said in an interview, recalling his own diversity training in the Air Force. “You’ve got to have some policies on diversity and racism and sexism.”

Conservative lawmakers may face similar hurdles persuading Republican moderates to undo a Pentagon policy offering time off and travel reimbursement to service members traveling out of state to obtain an abortion or related services, an attempt to equalize access after the Supreme Court overturned Roe v. Wade.

More than 50 House Republicans have signed on to amendments seeking to change the Pentagon’s abortion policy. But a handful have been outspoken in their criticism of the G.O.P. for attempting to push unforgiving policies.

“As a Republican, I want to make sure that we are showing compassion to women, and that we don’t drop the ball this week,” Representative Nancy Mace, Republican of South Carolina, said in an interview when asked about her party’s push to roll back the Pentagon’s policy on abortion access. “That’s my concern as it stands.”