When joining a new team as a product manager, is it better to have the right soft skills and have to learn the hard skills of the job? Or vice versa?
This reminds me of an interview question I got a very long time ago: "Is it better to have a bad team or a bad manager". In both cases, you'd rather not find yourself in either extreme. In both cases, there is no right or wrong answer and a lot depends on additional circumstances and assumptions. The answer will also depend on your value system and the experiences which have shaped your core beliefs about human aptitude and potential.
For the sake of argument, if I had to pick, I would first apply the same framework: which suboptimal option is more mitigatable.
I believe that most people have the capacity to learn the facts of the domain, the technical aspects, I.e. the hard skills, with sufficient effort and time. On some level, I see acquiring the hard skills in this contrived case akin to suceeding in a college course you know nothing about but are highly motivated to ace.
The soft skills can also be learned, but these are much more entangled with personality, self-awareness, communication style, etc., all of which develop and become ingrained over the years. They are harder to inculcate artificially or to undo as bad habits.
Poor soft skills can burn bridges and set the course of nascent relationships on the wrong trajectory, impacting your ability drive results far into the future. No amount of hard skills may be able to offset that. Good soft skills can even buy you time to get up to speed on the hard skills, and can get you critical early support from the team to actively help you get there.
This is why if I had to, I would pick the soft skills option.