A Texas stock exchange wants to take on New York. The odds aren’t good.

But that might not be enough to win business from the New York Stock Exchange and Nasdaq, which enjoy an effective duopoly on corporate listings and have withstood repeated attempts by others to break in.

Earlier this week, the venture announced that it had raised about $120 million to launch a Dallas-based stock exchange that would let companies save money on costs of complying with NYSE and Nasdaq listing rules. The TXSE, as it is known for short, plans to file an application to run a stock exchange with the Securities and Exchange Commission later this year, according to Chief Executive James Lee.

Lee said his exchange would be apolitical. But prospective investors who heard the TXSE’s pitch said it leaned heavily on criticism of Nasdaq’s listing rule that sets minimum targets for racial and gender diversity of their boards. The rule, approved by the SEC in 2021, prompted criticism from Republican politicians and a court challenge from conservative groups.

A spokesperson for TXSE denied that the venture’s pitch emphasized the board-diversity rule. Still, one of the TXSE’s most prominent supporters—Texas Gov. Greg Abbott—has stressed that the new exchange won’t promote a left-wing social agenda. He took a dig at Nasdaq’s board-diversity rule in a Thursday interview on CNBC.

“We need to make sure that Texas companies, and companies similarly situated, are not going to be cut off from capital markets in New York with policy decisions made from the left in places like New York,” Abbott said.

Elon Musk, a vocal critic of what he calls the “woke mind virus” as well as U.S. securities regulations, was among the business leaders who welcomed TXSE. Following news of the venture’s launch on Tuesday, the Tesla CEO tweeted: “Sounds promising.” Tesla, which moved its headquarters to Texas from California in 2021, is listed on Nasdaq.

Other big companies based in Texas include Exxon Mobil, AT&T and American Airlines.

The TXSE says it raised money from more than two dozen investors, including BlackRock, the world’s largest asset manager; electronic-trading giant Citadel Securities; and various individuals.

Citadel Securities is majority-owned by hedge-fund billionaire Ken Griffin, a major Republican donor. The firm’s investment decision was driven by a desire to increase competition among exchanges, according to a person familiar with Citadel Securities’ thinking.

BlackRock was previously known as a prominent backer of ESG—investing guided by environmental, social and corporate-governance concerns—though it has recently backed away from the term. Backing the TXSE might help BlackRock repair its image in the Lone Star State. Texas has put BlackRock on a list of companies that it considers boycotters of the fossil-fuel industry, prompting a state-education fund to divest itself of billions of dollars from BlackRock’s funds.

“BlackRock has been working to…eliminate the tarnish on their reputation,” Abbott, the Texas governor, told CNBC when asked about the firm’s investment in the TXSE.

A BlackRock spokesperson said the firm was supporting the venture to help improve liquidity and efficiency in U.S. capital markets.

Exchange-industry veterans doubted that the TXSE would succeed in making inroads into the business of corporate listings.

A core part of the venture’s pitch is that it will help companies save on the costs of compliance with onerous regulations. But the regulations governing public companies are largely set at the federal level, by the SEC, not by the NYSE and Nasdaq. Differences between NYSE and Nasdaq rules are generally minor, and any new listing rules must be reviewed by the SEC.

Moreover, NYSE and Nasdaq have listings teams that court companies around the world. Being listed on one of the two major exchanges has long been the sign of a company’s success—an embedded advantage that the TXSE will have trouble challenging, said Patrick Healy, CEO of Issuer Network, an advisory firm.

“These guys might be chasing a pipe dream here. Nasdaq and the NYSE aren’t just going to let someone eat their bacon,” said Healy, whose firm advises companies on which exchange to list on.

Healy expressed doubt that politics would prompt companies to switch to the TXSE. “It’s safe to say that a lot of people in Texas don’t like New York—it’s the political divide,” he said. “So I think people will listen to the TXSE’s pitch, but they won’t convert.”

The TXSE is hedging its bets by allowing companies to do dual listings, where they would be listed on both the NYSE and the TXSE, for example. It also plans to list exchange-traded products.

Past efforts to create a third exchange for U.S. corporate listings have gained little traction. IEX Group, the startup exchange operator made famous by Michael Lewis’s book “Flash Boys,” exited its listings business in 2019 after attracting only one company. The Long-Term Stock Exchange, a new exchange backed by Silicon Valley heavyweights, launched in 2020 with a plan to attract dual listings of companies focused on “long-termism” rather than short-term financial targets. Today it has only two listed companies.

“The listings business has long been a graveyard for exchanges trying to break into the NYSE-Nasdaq duopoly,” said James Angel, a finance professor at Georgetown University.

Write to Alexander Osipovich at alexo@wsj.com