The issue is with Sharepoint blog category view. The page should only show the posts which have been tagged with the category you click on, but I have found this not to be the case.
Here we go…
Navigate to the category.aspx page of the Sharepoint blog.
Add a Query string (URL) Filter web part.
Modify the query string web part settings. Query string parameter name must be Name.
Remove the filter from the posts web part.
Go into the Posts web parts settings, click edit the current view.
In the Filter section, change the option selected.
Now connect the query string web part to the posts web part.
You will get this little popup (you may need to allow popups). Select Category from the list.
Your category filtering should now work.