Shocking Miss Pilgrim, The (1947):

The Shocking Miss Pilgrim is a 1947 American musical comedy film in Technicolor written and directed by George Seaton, and starring Betty Grable and Dick Haymes.
The screenplay, based on a story by Frederica Sagor Maas and Ernest Maas, focuses on a young typist who becomes involved in the Women’s Suffrage movement in 1874. The songs were composed by George and Ira Gershwin. Marilyn Monroe made her film debut as an uncredited voice as a telephone operator.

Cynthia Pilgrim (Betty Grable) is the top typewriting student of the first graduating class of the Packard Business College in New York City, and as such she is offered a position with the Pritchard Shipping Company in Boston. There, she finds an office of men overseen by office manager Mr. Saxon (Gene Lockhart). When Cynthia introduces herself to company co-owner John Pritchard (Dick Haymes), he tells her he thought all expert typists were male and his policy is to hire only men. Cynthia asks for an opportunity to prove she’s as efficient as her male counterparts, but John refuses and offers her train fare back to New York.
John’s Aunt Alice (Anne Revere), an avowed suffragette, has the controlling interest in the company and insists that Cynthia be given a chance. Cynthia finds lodgings at Catherine Dennison’s (Elizabeth Patterson) boarding house, where she meets an eclectic group of tenants, including poet Leander Woolsey (Allyn Joslyn), artist Michael Michael (Arthur Shields), and musician Herbert Jothan (Charles Kemper).
John invites Cynthia to dinner but she prefers not to socialize with her employer. She does allow him to escort her to one of his aunt’s rallies, where she impresses the other women, despite John Pritchard standing up from the audience and asking her some awkward questions about management and labor getting closer together. When John’s mother asks her to dine with them on the evening of the Regimental Ball, Cynthia feels she won’t fit in with the woman’s social circle, so her rooming house companions coach her on how to behave unpleasantly, thinking the mother would be a snob. Cynthia is delighted to discover their efforts were unnecessary, because Mrs. Pritchard proves to be down-to-earth and a supporter of Cynthia’s desire to be treated equally in the workplace.
John begins to date Cynthia, and eventually they become engaged. He tries to persuade her to give up her involvement in the suffrage movement, but she insists she cannot abandon such a worthy cause. They break their engagement and she is fired from her job, but none of the people hired by Mr. Saxon to replace her please Mr. Pritchard. He and John go, in desperation, to a local school to find yet another candidate for the position. There, John discovers that its general manager is Cynthia, and the two are reunited in business as well as in love.