Lipman, 80, told The Times: “I would like to reassure him that I will not be arriving with a star of David on my forehead, nor am I trying to argue him out of his point of view.”
“He has to wake up and smell the grass. I have worked with actors for 60 years who often don’t share my politics. I don’t ask them, and they don’t ask me.”
Lipman said McCarthy was entitled to decide he did not want to work with her, but added: “But if he won’t meet with me, then he’s a coward.
“And if he doesn’t grow up, then he’s going to limit himself to working with just Mark Ruffalo and Javier Bardem for the rest of his career.”
The dispute arose over a single performance of Right Before I Go, which uses letters and poems about suicide to raise awareness and funds for people struggling with suicidal thoughts. The production transferred to London following a run at the Edinburgh Fringe.
Lipman also questioned McCarthy’s decision because he had attended the opening night of her recent production of Allegra only weeks earlier.
“He was pictured at the after-party and even posted glowing praise for the play and my performance on Instagram,” she wrote in The Telegraph on Wednesday.
“So I would love to know what has changed in the last six weeks. Has he become radicalised, and by whom?”
Lipman said she would rather discuss their differences face to face, even extending an invitation to McCarthy to meet her for hummus and mint tea.
“We can swap certainties about the world,” she wrote.
In her Telegraph article, she rejected any suggestion that she should moderate her views because of their effect on her career.
“I will not be bullied, nor will I allow anybody to tell me what to think,” she wrote. “If that affects their ability to work with me, as opposed to convert me to their point of view, then they are lily-livered.”
She acknowledged that the theatre world is largely politically progressive but said refusing to work with people who disagreed with her would undermine the principles of the profession.
“If we spit on art, we are being fascistic,” she wrote.
Lipman also admitted to once refusing to appear alongside Margaret Thatcher earlier in her career, a decision which she now thinks about and regrets.
“It was cowardly, stupid and ignorant. I could have sat with her and we could have talked about what we had in common as working women,” she said.
“I did not have to scurry out and leave, but I did. Even now, more than 40 years on, I think about it a lot.
“So, I confidently predict that Mr McCarthy will one day be appalled about his decision to pull out of Right Before I Go.”