I think WB may live and let live. Celebrities' personal drama tends to spill out into the public. There's little a studio can do to control that.
Disney fired James Gunn and then hired him back as soon as another studio gave him a job.
Jeremy Renner has also gotten bad press regarding his wife, but he's still Hawkeye.
Angelina Jolie actively tried to destroy Brad Pitt's reputation and career AND deny him access to his children but there she is in a Marvel movie.