When working with multiple hierarchies in a dimension, it is typical to apply a hierarchy filter to subsets to focus on only one of the hierarchies. That way, planners are not overwhelmed with all the parallel hierarchies.
Unfortunately, this only works, as long as the user who opens the report has access to the element specified in the hierarchy filter. Typically this is a root element. Planners don't have access to root elements (i.e. "total" elements) in dimensions that are restricted, so they get an error or a fallback mechanism kicks in, which results in a default element instead of the expected subset result.
Example: Cost Center with two hierarchies to allow better analysis with two different structures. The Report Builder decides, that the structure by function areas is the one relevant in this report, so they apply a hierarchy filter.
Having only limited access, some default element is presented instead of all the elements the user as access to within this parallel hierarchy.
Therefore, using a hierarchy filter is usually limited to using it only in dimensions that are not restricted. Hence, using parallel hierarchies only makes sense in dimensions that are not restricted.
This is a limitation that doesn't match typical use cases, where e.g. Cost Center - a common dimension with restricted permissions - is structured by different consolidations in parallel hierarchies (by legal entity; by function area; by division;...).
Even if the user doesn't have permission to the hierarchy filter element, it should be considered as part of the filter.