By David Benoit And Liz Hoffman

April 16, 2015 2:43 p.m. ET

As activist shareholders increasingly become a fixture of corporate America, battle lines are being drawn in the boardroom.

Take a recent dust-up on the board of Vail Resorts Inc.

Directors of the ski-slope operator this month forced out fellow board member Richard Kincaid after they discovered he had joined forces with activist investor Jonathan Litt, according to people familiar with the matter and a letter reviewed by The Wall Street Journal.

Mr. Kincaid and Mr. Litt weren’t planning to push for changes at Vail. Rather, they were aiming to take seats on the board of casino operator MGM Resorts International. The one link between the two companies: They share the same lead independent director, Roland Hernandez.

Shortly after Mr. Litt’s Land & Buildings Investment Management LLC nominated Mr. Kincaid and three others to the casino company’s board, Mr. Kincaid found himself in the cross hairs of Vail directors, including Mr. Hernandez and Chief Executive Officer Robert Katz, according to the people. He was uninvited from a scheduled three-day retreat for Vail directors and soon advised that he should either give up his MGM campaign or resign from Vail, the people said.

He decided to resign, midterm, after almost nine years on the board. The announcement was made last week, though it gave no reason for his departure. But in his April 8 resignation letter, reviewed by the Journal, Mr. Kincaid cited concerns he said were raised by Mr. Katz and other board members about his involvement in the proxy fight at MGM.

Messrs. Kincaid, Hernandez and Katz didn’t respond to requests for comment. A Vail spokeswoman said she wouldn’t comment on confidential board discussions. An MGM spokesman declined to comment.

Such boardroom rifts could become more prevalent as shareholder activists, who typically buy stakes in companies seeking board seats and agitating for changes, step up attempts to gain legitimacy among companies and other investors. As part of these efforts, activists such as Mr. Litt are courting directors with pedigree and gravitas to offer up as nominees. That is likely to set up battles such as that seen inside the Vail boardroom.

“It can be a double-edged sword,” said Marjorie Bowen, who has served on both corporate boards, including that of clothing retailer Talbots Inc., and dissident director slates. “Activists have upped their game and are nominating candidates with real industry and boardroom experience, and that’s been a key to their success. But those people have relationships that are much more far-reaching.”

Mr. Kincaid sits on a number of other boards. The 53-year-old was CEO of Equity Office Properties Trust when the commercial landlord was acquired in 2007 by Blackstone Group LP in one of the biggest buyouts ever.

He is just the latest established director to sign on with an activist. In the past year, Trian Fund Management LP placed former H.J. Heinz Co. CEO William Johnson on the board of PepsiCo Inc., Corvex Management LP tapped real-estate mogul Sam Zell for a proposed slate of directors, and Third Point LLC put Steve Miller, the nonexecutive chairman of American International Group Inc., on the board of Dow Chemical Co.

Offering more experienced directors as nominees has enabled activists to make better inroads onto boards, advisers on both sides said. Last year, activists won at least a partial victory in 73% of all fights for board seats and other changes, a record rate according to FactSet. Activists have also gained entry onto boards without having to wage proxy fights, including at large companies including PepsiCo and Dow Chemical.

But activist campaigns remain unnerving to some on the receiving end of them, and some corporate directors and officials continue to regard the investors as adversaries.

“Having somebody show up out of the blue and say, ‘here’s what you’re doing wrong’ isn’t always well-received, even if the ideas themselves have merit,” said Jeffrey Shapiro, a lawyer at Lowenstein Sandler PC who has advised both investors and companies in activist fights.

Last week, a director at Staples Inc., Justin King, said he would give up his seat at the end of his term in June to protest the company’s decision to add Kunal Kamlani to its board. Mr. King said Mr. Kamlani, who was nominated by activist investor Starboard Value LP, was neither “suitably qualified nor independent” and questioned whether he would serve the interests of all shareholders at the office-supply retailer.

Mr. Kamlani, who has served as chief operating officer of Prestige Cruise Holdings Inc., said he researched Staples extensively before agreeing to join its board and said the board itself was equally thorough with his nomination. Starboard declined to comment. Staples thanked Mr. King for his service and said it reviews board members to add different skills and to the benefit of all stockholders.

Being a director is a rite of passage for many corporate officials as they head to retirement. Many serve on several boards, receiving hundreds of thousands of dollars a year in fees and other compensation. That may give some directors pause before joining forces with agitators.

Mr. Kincaid is giving up some rich perks. Vail Resorts directors were paid about $285,000 on average in 2013 in cash, stock and other awards, according to its most recent proxy statement. They also received a $40,000 annual allowance to be used at the company’s resorts, which include high-end properties in Breckenridge, Colo., and Park City, Utah.

Vail’s board guidelines, available on its website, said directors should tell the chairman of the governance committee—in this case, also Mr. Hernandez—“in advance of accepting an invitation to serve on another public company board.”

While she wouldn’t comment on the reasons for Mr. Kincaid’s departure or whether Mr. Kincaid violated that rule, the Vail spokeswoman said the company “has a set of public guidelines for its board of directors that ensure strong governance and serve the best interests of its shareholders, and all directors are expected to adhere to them.”

Write to Liz Hoffman at liz.hoffman@wsj.com and David Benoit at david.benoit@wsj.com