Can a postdoc change his/her supervisor in Sweden?
(I'm faculty at Chalmers University of Technology, a well-known private university in Gothenburg, Sweden)

The pragmatic question (whether it's a good idea to change supervisors mid-flight) is covered well by posdef, I'll focus on the legal angle here.

As you mention, PhD students have quite some rights in Sweden, but this is mostly because they are in a special type of employment largely governed by Swedish university law. This is not the case for postdocs - postdocs aren't students and they are not faculty (for which the law also knows some special privileges). Fundamentally, postdocs are just "employees", similar to research engineers, secretaries, or university accountants, and hence their tasks, rights, and privileges are exactly what the university has defined in their job profile. At Chalmers, I am not aware that there is any formalized "right" to be assigned a different supervisor. I suspect the situation in other universities is similar, but you may want to check your own contract first.

That said, and to echo the other answers a little, changing your supervisor is hard. Really hard. Even as a PhD student, when the law is on your side. Funding is a huge issue, but so is the fact that faculty tends to be sceptical of taking on students/employees where one of their colleagues has already made bad experiences. As always, there are exceptions, but in general you should figure out which faculty would take you on and take over your funding before talking publicly about changing supervisors. It's better to have a normal working relation with a supervisor that is not ideal, than to have an advisor who has been assigned by the department because nobody else took you on.