Good for her daughter for writing in on her behalf, and for the Yankees for handling it beautifully. So cool.
As for women playing pro baseball - a couple have. The first was Lizzie Arlington, followed by Jackie Mitchell.
https://calltothepen.com/2017/07/05/baseball-history-lizzie-arlington-becomes-first-female-player/
Arlington came to prominence as a part of the Philadelphia Nationals reserve team. Discovered out of the Pennsylvania coal region, she played baseball with her father and brothers against other competition. She would end up playing second and pitching for the Nationals, where she proved to be just as good as her male counterparts.
History was made on this day in 1898 when she suited up for the Reading Coal Heavers, now known as the Reading Phillies, of the Atlantic League. With Reading holding a 5-0 lead over the Alentown Peanuts, Arlington entered the game in the ninth inning.
Her appearance had quite the rocky beginning. Arlington allowed two hits and a walk to load the bases before retiring a batter. However, she settled in after that, retiring the next three batters and emerging without allowing a run. Newspaper reports said that Arlington did not have the command needed to perform well at that level, but nonetheless, her outing was a success.
Arlington was expected to appear against the Hartford team, but was not allowed to. Local authorities forced Reading to cancel her appearance, as Hartford was concerned about losing to a female. Afterwards, Arlington disappeared, fading away into obscurity.
It has been claimed that women are 'too delicate' for the game, but it could be that men are often the ones who have a hard time competing against women.
https://howtheyplay.com/team-sports/Jackie-Mitchell-was-the-only-professional-Female-Baseball-player-to-Strike-Out-Babe-Ruth-and-then-Lou-Gehrig
Jackie Mitchell was born on August 29, 1913. Her full name was Virne Beatrice Mitchell. She was only the second professional female baseball player in the history of the game. The first was Lizzie Arlington. She pitched in a game for a team known as the Reading Coal Heavers in 1898. [snip]
The Chattanooga Lookouts were scheduled to play an exhibition game with the New York Yankees. It was played on April 2, 1931, after being rained out the previous day. Jackie Mitchell took the mound in the first inning as a relief pitcher. The starting pitcher was Clyde Barfoot, and he'd just given up a single and a double. The next two scheduled batters were baseball legends Babe Ruth and Lou Gehrig.
Mitchell was throwing her trademark sinker. Her first pitch to Babe Ruth was called a ball. During the next two pitches, Ruth swung at both and missed. He asked the umpire to inspect the ball. A new one was thrown out to Mitchell by the umpire. The fourth pitch delivered to Ruth was a called third strike. Ruth was furious. He glared at the umpire and started screaming at him. Other Yankee players had to come onto the field and lead him away. He was calm by the time he reached the bench.
During this time, the crowd was screaming their approval for Mitchell. After the game, Ruth told a Chattanooga newspaper that he didn't know what would happen if women were permitted to play baseball. He felt they were too delicate, and it would be too difficult for them to play every day. [more]
Another good article covering Jackie Mitchell:
https://www.mlb.com/news/meet-jackie-mitchell-the-girl-who-struck-out-babe-ruth
The misogynists -- or at least Mitchell's detractors -- had their day nonetheless. Elsewhere in The Times, it was written that Ruth "performed his role very ably" by striking out and that Gehrig "took three hefty swings as his contribution to the occasion," the occasion implied being yet another promotional stunt from Engel in which the sluggers allowed Mitchell to strike them out. The fact that it was originally scheduled for April Fools' Day was another data point cited against the authenticity of Mitchell's feat.
If Gehrig or Ruth did strike out on purpose, neither owned up to it in subsequent years. While it would surprise no one if Ruth were in on such a setup, it would be out of character for Gehrig. Given Mitchell's tutelage from Vance and the fact that her sidearm lefty delivery gave her the platoon advantage against both sluggers, it's not a huge stretch that she struck them out on merit. [snip]
It was widely reported that baseball commissioner Kenesaw Mountain Landis voided Mitchell's contract in the aftermath of the game, citing that baseball was too strenuous for women. Though there is no proof of this, it wouldn't exactly be out of character for Landis.
