Ingrid Newkirk, co-founder and president of People for the Ethical Treatment of Animals, flew to Silicon Valley earlier this year for a long-planned speech to Google employees. It wasn’t until she sat waiting in a parking lot that a call came through notifying her the event was canceled.

Ms. Newkirk had been invited by some employees to discuss her view that animals can be subject to prejudice just as people can, as part of the company’s “Talks at Google” series. Another group of employees said the topic was offensive to humans...