Removing a row from a view depending on the user currently logged in
This isn't a views' problem. I'm assuming that the non-core users should not have access to the content that has the core-team tag anywhere (not just in the specific view). That's because if you use a "hack" to remove the result from the view, someone entering the specific blog post's url directly in his browser would take him to the node.

What you actually need to do is use the Taxonomy Access Control module to restrict access to the "core-team" tag. When you do that, the non-core user will not have permission to view the content tagged as "core-team", so the view will not display these results either (assuming that in the access restrictions of the view you left the default value of: "Permission").