Be a voice of logic and reason. Don't let your partner suck you in to any negativity about his ex. See the difference between what he says she is and how she behaves. Don't just side with him on everything - if you consider what mum says is in the best interests of the child, say so and say why. If your partner can rely on you to be a voice of reason, to help him see the other side of an argument, the child will experience less conflict in his life.
In my ex's case, he has a partner who has never met me and we have never spoken on the phone so she has no direct experience of me. She doesn't seem to recognise that there is literally no one at all in my ex's social circle that knows me. If his friends don't know me, he can say what he wants about me and there is never going to be any challenge. She has listened to him, however, and the impact on our children is massive because their home is constant negativity about me - what I wear, what I eat/don't eat, how often I go out, where I work....the questions are endless and never met with 'oh, good for mummy!' but rather 'why would a place like that employ someone like her?' or 'it's illegal to give you a sandwich for your tea' or 'she needs to get up earlier and drop you off at school' when they know nothing at all about what time I start work and restrictions based on childcare opening hours etc. etc. etc.
What she doesn't think about is he sees his children regularly without any interference from me. That he doesn't pay maintenance but he stills sees them. That there are no 2am texts or any texts or emails (literally texted him 32 days ago just looking now) so if he's on his phone the whole time, it's not me! What she doesn't see and hear says way more about me than what he says about me, in other words.
Of course, there may be good reason for any ex to be considered awful and un-cooperative. And in those cases, support for your partner is absolutely valid. But the skills to read between the lines is essential in helping manage long term co-parenting because there will be conflict and your opinion will be sought.