Live Action says the blocked content makes up the very core of its message.
The Sept. 11 letter requested that the company reinstate the organization's ability to promote tweets to a broader audience beyond its tens of thousands of Twitter followers.
Live Action's allegations come at a time when Facebook, Google and other social media companies faced accusations of overstepping their role as hosts or moderators of the public square, and straying into the realm of censorship.
But setting standards for acceptable speech becomes especially murky when it comes to paid advertising on some of the most divisive issues in America -- as it does in the dispute between Twitter and Live Action.
And companies have the right to set their own guidelines, even if it means blocking ads promoting controversial political or social issues.
Live Action claims Twitter, which has more than 300 million active users a month, went too far.
"This wasn't about one issue with one aspect with one ad. This was about the entirety of our message, from ultrasound images of life in the womb to criticism of abortion facilities," said Lila Rose, Live Action's 29-year-old president who founded the group when she was 15.
"The heart of Twitter's self-named purpose is to 'give everyone the power to create and share ideas and information instantly, without barriers,'" said Rose, quoting the company's mission statement. "They are completely violating that."
A Twitter spokeswoman denied that the company censors advertisers based on their political viewpoints. She said Twitter had advertising relationships with a number of socially and politically conservative groups, including another prominent anti-abortion group, the Susan B. Anthony List.
But Twitter does set a higher bar for advertisers than regular users when it comes to the type of content it will promote.
The spokeswoman said the company has clear, transparent rules that all advertisers must follow. Twitter's extensive advertising policy states that ads must be honest and accurate. The guidelines prohibit advertisers from misleading people with sensationalized language and deceptive claims. And Twitter bars content that could offend or shock people, among other directives.
The spokeswoman said the rules are equally applied to all advertisers, no matter their political viewpoint. She would not address the specifics of Live Action's allegations or details of its ads, including why the content was banned.
In a May 18 email to Live Action, Twitter's political and advocacy sales team told the organization that its ads violated Twitter's sensitive advertising content policy, which prohibits "inflammatory or provocative content which is likely to evoke a strong negative reaction" as well as content that is shocking, disturbing, or offensive.
Twitter gave Live Action two choices to become eligible for advertising in the future: remove "sensitive content" from its website and Twitter feed, or create a Twitter handle linking to a new website without the offending content, according to the email exchanges provided by Live Action that The Washington Post has verified.
Among the "sensitive content" Twitter objected to that would have to be wiped from Live Action's website and Twitter feed: videos of the organization's undercover investigations, images and videos of abortion procedures, a petition to defund Planned Parenthood, and fetal ultrasounds.
Pete Slevin, one of the attorneys representing Live Action , characterized Twitter's parameters for reinstating the organization's ability to advertise as "unusual."
"It's not just that Twitter is saying, as a practical matter, that we're going to 'regulate' your Tweets, they're also seeming to 'regulate' what Live Action is posting on its own website," Slevin said.
Rose said Live Action has spent about $50,000 on promoted tweets since it began advertising on Twitter in 2013, and some of the blocked ads had run in previous years without incident.
"Seems like for reasons unknown, Twitter has erred recently on the side of avoiding offense," said Slevin, who was retained in July.
Twitter suspended Live Action's ability to promote tweets in 2015 and blocked Rose's account -- which has nearly twice as many followers -- from advertising earlier this year. Both accounts are still allowed to tweet to their followers.
One tweet Rose said was rejected for promotion featured a photo of a fetus captioned "I am not a potential human. I am a human with potential." Others targeted Planned Parenthood, falsely accusing it of selling baby parts for profit. Another linked to a petition to stop taxpayer funding of Planned Parenthood.
Rose said her organization has successfully run versions of the ads banned by Twitter on Facebook. It also advertises on YouTube and Instagram. A spokesman for Facebook would not confirm her assertion.
Wendy Melillo, an American University strategic communications professor who studies public service advertising, said the Twitter controversy with Live Action is reminiscent of a 2010 Super Bowl ad featuring star quarterback Tim Tebow and his mother, who famously ignored advice to have an abortion.
The 30-second ad, sponsored by Focus on the Family, a conservative Christian group that opposes abortion, urged viewers to "celebrate life" and directed them to the group's website "for the full Tebow story."
CBS drew backlash before the ad even aired because the networks generally had a policy not to air polarizing advocacy or political ads, Melillo said. Anti-abortion advocates were angry at reports that the ad had been watered down to fit the networks' standards. Abortion rights groups thought it gave their opponents an outsized platform during the most-watched television event of the year.
"Abortion is one of those hot button controversial wedge issues that divides us, and Twitter has the right to accept or reject ads based on its own standards," Melillo said. "At the end of the day, Twitter is a business and seems to be following a similar pattern long-established by the networks."
Live Action said it does not advertise on television or in print media, and believes it can command the largest audience on social media.
The tech companies all have their individual advertising standards, and Melillo said the industry as a whole risked appearing inconsistent, given how broad and subjective the rules can be.
"There's a danger that they could appear to be biased on one side of the abortion issue or the other," Melillo said.
Other anti-abortion groups have also accused tech giants of stifling their ability to spread their message.
Google several years ago removed web search ads for "crisis pregnancy centers" for violating the company's policy against deceptive advertising. The majority of the centers advertised abortion services when, in fact, they provided information about alternatives to abortion.
The Susan B. Anthony List, which promotes legislators and laws that seek to limit abortion, said Twitter rejected several of its ads in the spring for violating its "health and pharmaceutical products and services policy."
The tweets included one from its president, Marjorie Dannenfelser, that said, "Let's envision 'A Day without Abortionists'" -- a play on the "Day without Women." Another displayed a graphic of Mother Teresa saying that "Abortion is profoundly anti-women."
Twitter suspended the organization's ability to advertise for several days. Mallory Quigley, a Susan B. Anthony List spokeswoman, said the organization has now "reached an uneasy peace" with Twitter. She said her group stands with Live Action against what it called censorship by Twitter.
"Their voice is far too important to be silenced," Quigley said. "We remain vigilant about anything that could threaten our ability to effectively communicate the pro-life message."