Ed Andrieski—AP
March 25, 2014 5:30 AM EDT

The U.S. Supreme Court on Tuesday will tackle a pair of court cases that straddle some of the most charged topics in American politics. The cases could have ramifications for issues such as religious liberty, contraception, gay rights, employment discrimination, health-care reform and corporate personhood. In this smorgasbord of wedge issues, there’s something for every political faction to love or loathe — but some of the groups with the most at stake have been curiously silent.

The cases brought by Hobby Lobby, a national chain of craft stores based in Oklahoma City, and Conestoga Wood, a cabinet-maker from Pennsylvania, test the question of whether for-profit corporations can invoke the constitutional guarantee of religious freedom to avoid the so-called contraceptive mandate in Obamacare. Hobby Lobby is owned by observant Christians who signed a pledge to run their business by religious principles. It closes up on Sundays, eschews racy products and pipes Christian music through its shops. In a similar vein, Conestoga Wood is owned by a family of conservative Mennonites who operate their business in accordance with their religious beliefs.

The plaintiffs filed suit against the Obama administration, objecting to the Affordable Care Act’s requirement that companies provide employees no-cost insurance coverage for contraceptives. The companies contend that certain forms of contraception, such as the so-called “morning-after pill,” violate religious prohibitions against abortion. The Court’s decision is expected to come in June.

Since the issues are explosive, it’s no surprise the case has come with substantial fanfare. It generated more than 80 amicus briefs from concerned parties—among the highest tallies ever, according to the Becket Fund for Religious Liberty. Women’s rights organizations, religious groups and atheist coalitions are all using Tuesday’s oral arguments to launch a lobbying blitz.

That’s why it’s so surprising that America’s leading business lobbies have remained silent on the matter. The U.S. Chamber of Commerce, a frequent player in Supreme Court litigation, opted not to join the legal debate over the two cases. Asked whether it had an opinion, Rachel Parker, director of legal communications for the Chamber’s litigation arm, declined to answer. “We didn’t file [a brief] in this case and generally don’t discuss the specifics for why we do [or] do not get involved in a particular case,” Parker says. The National Federation of Independent Business, another conservative association, did not respond to TIME’s inquiry about whether it took a position on the case.

These influential lobbying outfits may be opting to sit out a case with major implications for their members because many businesses see its electrified politics as a threat to future profits. Aaron Katz, a partner at Ropes & Gray LLP, represents a coalition of nearly two dozen corporate and criminal law professors who reject Hobby Lobby and Conestoga’s arguments that secular, for-profit corporations can invoke the religious protections afforded to their owners. The group argues that shareholders who choose to organize themselves as a corporation do so in order to get certain benefits, such as shielding themselves from personal liability. That decision establishes a separation between the corporation and its owners that the Court’s rulings in cases like Citizens United do not erase. “The shareholders cannot decide it suits them on one day to be a corporation,” Katz says, “then turn around on day two and say it benefits us for the corporation to take on our personal identities.”

But even executives who may sympathize with Hobby Lobby or object to the contraception mandate may be leery of jumping into a debate with the potential to alienate their customers, incense their workforce or embroil corporate boards in controversial disputes. “This is one of those situations where businesses realize they can’t isolate, ostracize or do things to offend their employees or customer base,” Katz says. “Hobby Lobby may win this case, but they could lose customers because of it. I’m not sure how many other businesses want to take that risk.”

The case also presents challenges for the Republican Party, whose base is studded with both influential religious groups and their business counterparts. Social conservatives have made the court cases a battle cry, and several dozen GOP lawmakers have sided with the plaintiffs on First Amendment grounds. That includes the nation’s top elected Republican, House Speaker John Boehner, who released a statement Monday afternoon urging the Court to “reverse this attack on religious liberty and reaffirm our founding principles.”

But much of the business-oriented Republican establishment, as well as the GOP’s political committees, have been relatively quiet about the case. The National Republican Congressional Committee, which has made Obamacare the centerpiece of its messaging campaign for the upcoming midterm elections, did not respond to a question from TIME about its position on the contraception mandate.

The legal challenge to the contraception mandate “highlights just another problem with Obama’s one size fits all solution to healthcare,” says Kirsten Kukowski, a spokeswoman for the Republican National Committee. “It infringes on the free exercise of religion guaranteed by our constitution.” But beyond that statement, the RNC has not done much to bring the case to the public’s attention.

The Republicans’ decision to downplay the challenge serves to underline the tension within the party’s base. While religious conservatives are determined to fight and refight wedge issues like abortion and gay marriage, much of the GOP establishment is eager to move past divisive debates and focus on broadening the party’s appeal to an evolving electorate. Religious freedom is a cause for the former faction and a tricky topic for the latter. Only a month ago, Arizona’s Republican Governor Jan Brewer was torn between the two camps when her state legislature passed a bill that would have allowed the state’s business owners to deny service to gay and lesbian customers on the basis of their religious beliefs. Under pressure from business interests, Brewer ultimately opted to veto the bill.

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Write to Alex Altman at alex_altman@timemagazine.com.

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