(Recasts; adds context in paragraph 3; adds in paragraph 6 that a U.S. appeals court upheld the transfer of SpaceX's lawsuit)

March 5 (Reuters) - A U.S. labor board judge on Tuesday began a hearing in a case accusing rocket maker SpaceX of illegally firing eight engineers for criticizing CEO Elon Musk and accusing him of sexist conduct in a letter to company executives.

The case before National Labor Relations Board Administrative Law Judge Sharon Steckler in Los Angeles prompted SpaceX to file a lawsuit in January seeking to block it from going forward by claiming the board's in-house enforcement proceedings violate the U.S. Constitution.

Starbucks, Amazon.com and Trader Joe's, all of which are facing nationwide union organizing campaigns, have raised similar arguments in pending board cases. If any of the companies are successful, it could severely limit the agency's ability to hear cases involving allegations of illegal labor practices.

The NLRB's general counsel, which acts as a prosecutor, claims SpaceX violated U.S. labor law by firing the engineers in 2022 after they circulated a letter accusing Musk of sexist conduct and claiming the company tolerated discrimination against women. SpaceX is accused of violating the National Labor Relations Act, which protects workers' rights to band together and advocate for better working conditions.

The engineers have separately filed complaints with a California civil rights agency accusing SpaceX of tolerating sex discrimination and retaliating against workers who complained.

SpaceX has denied wrongdoing while attacking the labor board's core functions in the lawsuit, which it filed in federal court in Texas. A judge last month transferred the case to California, and a U.S. appeals court on Tuesday rejected the company's challenge to that decision.

Steckler on Tuesday said the hearing would be procedural, focusing on challenges by the board and SpaceX to subpoenas issued by each side. Steckler will not hear testimony or opening statements on Tuesday.

If SpaceX loses, it could be ordered to reinstate the workers and compensate them for lost pay and benefits. Steckler's decision in the case can be appealed to the five-member board and then a federal appeals court.

SpaceX did not respond to a request for comment. The company is represented by lawyers from law firm Morgan Lewis & Bockius, including John Ring, who was the chairman of the NLRB during the Trump administration.

SpaceX had asked to put off the hearing pending the company's bid in the Texas court to block the labor board case from moving forward. An NLRB regional director last month denied that motion and the five-member board, which has one vacancy, upheld that decision in a single-page ruling.

In its lawsuit, the company claims the labor board's administrative process for hearing cases involving illegal labor practices violates its constitutional right to a jury trial. SpaceX also says limits on the president's ability to remove administrative judges and board members are unconstitutional.

The labor board has said in court filings that removal protections similar to those for board judges and members have been upheld by the U.S. Supreme Court, and that the right to a jury trial does not extend to cases brought under federal labor law. (Reporting by Daniel Wiessner in Albany, New York, Editing by Alexia Garamfalvi, Lincoln Feast and Jonathan Oatis)