TLDR: It will depend very heavily on the funding situation.
A reasonable guess as to why there is a clear remark about the PhD students and not about the postdocs is that how postdocs are employed varies significantly.
Without having any proof, I would guess that you can't change your mentor however you like if s/he is paying you. Because why would you have that right, it is that person's own funding. In that situation your best bet (besides trying to find a resolution) is to quit and apply for a new position. Or better yet, apply for new positions and quit when you find one.
If you are bringing your own money, then you would have more flexibility, although it would still be an unpleasant move if you just bail out and start working down the aisle or the next floor.
That being said, you can in general not be forced to submit an article you are not happy with. Because you can always get it pulled (or your name removed) if you are not OK with it's content. That creates bad rep for the group and the paper in question, so I would be willing to guess that it's not really a common situation. More likely, you and the PI has differences of opinion as to why the paper should (or should not) be submitted, and if that's the case it's generally a better idea to try to understand each other rather than fight it.
You can however be forced not to submit a manuscript, or prevented from going to a conference, and I would say it happens relatively often. Usually not it harsh terms, but also that sometimes. That is part of the employment, that would happen anywhere and it's important to try and find constructive solutions. The comment by @lighthouse_keeper is on point, if you try to go down that route, you are burning bridges and you are the small fish in this particular case.
EDIT following OPs comment:
Re: the role of a postdoc
When a group leader gets funding, it's typically from a grant (exceptions exist but lets put that aside for the moment). Grants are written for specific subjects with usually well-defined tasks and goals. In the context of these tasks and goals, one or more postdoc positions might be opened.
So when you are a postdoc, you are taking on a role in that lab that fits their goals and targets, with the implicit assumption that whats good for the lab is also good for you. In other words, it's implied that carrying out your research project there is beneficial for both parties, meaning you choose to do your post-doctoral research there. If that is not the case then obviously it's not a good situation.
Within the context of that project and academic code of conduct, the group leader does have the privilege to direct the project as s/he sees fit. If your disagreements are fundamentally scientific (i.e. not related to bullying, fraud or something similar, which would typically violate the university's code of conduct) I don't see how you'd argue for a valid reason to change to another group, while keeping your current position.
Re: the comparison to a PhD student position
In comparison to a postdoc position, the university and the faculty is an active stakeholder when a PhD position is announced. In Sweden, most (all except a couple) universities are government institutions. So by being a fully employed PhD student you are a state employee, besides being a student. In this case the university (and by extension the state) has accepted you to a degree of higher education. If your supervisor cannot teach you well, for one reason or another, you are entitled (within reason) to ask for a change.
As you see there are some fundamental differences in what the employment is, what is being offered. I would not necessarily say that your rights are more limited, essentially it's not really a "right" to be able to change your manager. Your rights as it pertains to social security, healthcare, insurance, paid holidays, paid parental/sick leave etc apply regardless if you are PhD student or postdoc, as long as you are actually employed and not on a stipend.