Product management involves a lot of conflict, both within-team and between-teams. I've found the utility of conflict typically hinges on the underlying trust (or lack thereof) between those engaging in the conflict. Trust in one another as people (is this person going to screw me over?) and trust in one another’s capability (is this person competent?)
Building trust is usually much easier within teams, which is why intrateam conflict is invariably more fruitful than interteam conflict. I'm a strong believer that this is why so many orgs struggle to work effectively across programs. The trusting foundation isn't there to permit constructive conflict, meaning people bumble along in artificial harmony; achieving mediocre outcomes.
First, the obvious. Trust is so incredibly important. I truly believe we enter work relationships with a combination of trust for our teammates AND the collective weight of past conflicts AND whatever biases we have about roles & responsibilities. This is why you’ll need to work to increase and preserve trust and confront your own stereotypes of those around you. Second, product managers need to be especially aware of how their language can be interpreted (especially when they and their teammates are stressed and/or impatient). This is why I believe designers and engineers who transition to the product manager role will have a bit of an edge: they know how things might come off.