“Google has these values, and with our talks, we have to align with these values,” a Google employee told Ms. Newkirk, according to a transcript of the call.

Ingrid Newkirk is carried off by law enforcement after a protest to stop the sport shooting of hundreds of pigeons, one of her best-known protests. PHOTO: PETA

Such is the climate inside the tech giant, where fractious groups of employees have turned the workplace into a virtual war zone of debate over all manner of social and political beliefs. Google has long promoted a work culture that is more like a college campus—where loud debates and doctrinaire stances are commonplace—and today its parent, Alphabet Inc., GOOGL 0.35% is increasingly struggling to keep things under control.

“Activists at Google” helped organize a rally critical of President Donald Trump’s policies. “Militia at Google” members discussed their desire to overturn a prohibition on guns in the office. “Conservatives at Google” allege discrimination against right-leaning job candidates. “Sex Positive at Google” group members are concerned that explicit content is being unfairly removed from Google Drive file-sharing software.

“Googlers For Animals” invited the PETA president, only to be undercut by members of the “Black Googler Network.”

Google’s broad corporate culture has long leaned Democratic, and that’s reflected in internal debates that often pit left-wing causes against each other. Donations by its employees to Hillary Clinton’s presidential campaign outnumbered contributions to President Trump’s campaign 62 to 1, and former Alphabet Executive Chairman Eric Schmidt helped the Clinton campaign with data analysis. Less numerous, but increasingly voluble, are groups of conservative employees reacting against what they see as a Google’s political orthodoxy.

Beyond the internal debates are lawsuits, several since late last year, including legal actions from female employees alleging pay discrimination against women; from male ex-employees and potential new hires claiming bias against conservative white men; and from a transgender engineer who said he was fired for making derogatory statements about what he called white male privilege. All this comes on top of a very public controversy last August when Google fired a software engineer, James Damore, who wrote an internal memo saying gender differences might have something to do with women’s under-representation in the tech workforce.

Politicians, media and consumer groups are raising questions about how giant tech platforms such as Google, Facebook Inc. and Twitter Inc. make difficult decisions on issues of free speech that potentially affect billions of users.

Google, a crucial part of the internet’s behind-the-scenes police force, is struggling simultaneously to curate a cacophony of voices within its own abode and to define what is allowed in search and on YouTube. Google engineers are increasingly trying to refine the algorithms that block content for being hateful, extremist or dangerous, moves that also have triggered complaints of bias.

A Google spokeswoman said the last-minute quashing of Ms. Newkirk’s talk is seen internally as a failure to properly vet speakers. Since the cancellation, Google has formed a group of employees whose job is to review speakers in advance. Google also has published new guidelines for acceptable content in Talks at Google. Her speech would be prohibited under the new rules, which aim to make all employees feel included, said the Google spokeswoman.

Many companies have struggled to strike a balance between employees’ right to share their opinions and the maintenance of a cordial and equal workplace. In the run-up to the 2016 presidential election, Facebook dismantled an internal discussion board for political debate after it degenerated into racist and sexist comments, The Wall Street Journal reported.

Some companies have decided it is counterproductive to let employees form affinity group