I am a postdoctoral with governmental grant, means that it is not a grant from a research supervisor for a specific research project. Of course, when I was applying for this grant I was asked to connect with one of the professor in university X and I provided a research proposal. During working on the research related to my proposal, I am working on some other aspects which are not far from my proposed research in cooperation with some other scholars and professors outside of my university. I would like to ask your opinion on whether it is normal for postdoctoral researchers to have collaborations with other people as well?
I would like to ask your opinion on whether it is normal for postdoctoral researchers to have collaborations with other people as well?
Our opinions don’t matter. The professor in charge of your grant is considered your supervisor, and whether it’s okay for you to spend significant time on outside collaborations depends on, and only on, the professor’s opinion. It’s likely okay, and yes it is somewhat normal at least in some disciplines (e.g. math), but you should simply ask them.
How independent a post-doc can be depends on a lot of things, but funding is one of the more important ones. Since the institution you will be working at isn't funding you, they have little (but not zero) control over you.
However, and very important, is that collaboration is a good thing. A very good thing. It can boost your future prospects tremendously, both for getting a permanent position and for continuing to do good research.
But, you don't need to feel that you must submit to the views of others if you differ in some way. But those sorts of relationships are destructive potentially in any case.
Think of your colleagues as collaborators, not superiors or inferiors. Share ideas. Build a backlog of ideas for future research. Build a large cohort of collaborators. But, you have the freedom to set your own path.