"Legitimate grievances" refers to valid complaints or hardships that are justifiable and reasonable. It implies that the concerns or issues raised by someone are fair and deserve attention or resolution. Full definition
One challenges facing lawmakers is that some members will have legitimate grievances about not receiving enough funding to respond to disasters in their areas. (vox.com)
There is a pretty legitimate grievance that First Nations along the pipeline route have. (macleans.ca)
But are there legitimate grievances in the case of the Brexit referendum? (blog.politics.ox.ac.uk)