I have found that once you create a shared parameter, assign it to a family under a particular category like "dimensions" or "data", and then load that family into the project environment, then that shared parameter tends to stick to that category in the project.
For example, if I change the shared parameter category from "General" to "Structural" within the family editor, then load that family back into the project, when I open the properties dialogue for that family in the project, the shared parameter is still listed under the "General" category and not the "Structural" category. And there is no way to change the shared parameter category within the project environment from the Manage>Shared Parameters tab.
I have found however, that if you create a dummy model-in-place component within the project environment, and within the editing mode for that component add the same shared parameter to it from the "Family Types" panel, assign the shared parameter to the new category (in this example "Structural"), then "Finish Model" and check your original family again, the shared parameter will have moved from the old category that it was stuck in ("General"), and to the new category you moved it to ("Structural"). In fact this method of assigning the shared parameter to a category within a model-in-place family/component will always overwrite the shared parameter's category for all families that use it in that project to the latest category that you assign it to in any the model-in-place family.
To summarize, changing a shared parameter's category within the family environment has no effect once you load that family back into the project environment. The only way to change the shared parameter category is to change it from within a model-in-place family in the project environment.
You can then delete the dummy model-in-place family and the shared parameter category will stick to whatever it was just assigned as within the project.
This is kind of a non-intuitive and weird way to control what category shared parameters appear in, but it's the only way I have found that works. Anyone have a different tip/experience with this?
I personally think that shared parameter category should be allowed to either
A) Not be controlled by the project, but rather assigned to whatever category the family has put it in, regardless of what other families categorize it as. This "assign-by-family" approach, makes more sense to me since we typically assign categories within families, not the project and when editing a family it can be confusing to find the parameter in a different category in the family than what it is in the project.
B) If the category is to be controlled by the project, then at least let us change the category from the Manage>Shared Parameters panel.
