Surely advertisers are wise to this. A year or so ago one of my more "woke" Fb friends was pushing some sort of advertiser boycott of the Daily Mail. Advertisers want to sell stuff, and will primarily interested in reaching potential consumers.
If they feel that the vehicle for their message has become tainted and that an association with that vehicle is not in their interests, like with Breitbart, or as happened when department stores dropped the Ivanka Trump lable, they will withdraw. But presumably Birds Eye are not so blinkered by PC that they cant understand why mums might be concerned the child protection issues around gender self-id and why mums want a forum for discussion.
Actually I think that MN's super stardom over protecting the right to free speech has done their image no harm at all and that their advertisers stand to benefit from association with the site.