She didn't seem to mind River though?
Good point. Maybe the plot requires it now?
Why would the TARDIS have a problem with River? The only real reason her story is complicated is because the Doctor always meets her in the wrong order. There is nothing inherently problematic about her existence.
Clara, on the other hand, has died at least twice in two completely different time periods, yet is also alive and kicking as a normal 21st Century girl.
River's existence might be complicated, but Clara's is impossible.