Has non animal rennet. Kosher?
Not kosher
Do you know why some Tillamook kosher some not? Special run?
Do you know of any with kosher supervision? Because the above photo is certified by the Islamic council of America. Not exactly one of our approved Hechsherim. 
Their kosher certified cheese is the same cheese as the medium Cheddar, but they have a mashgiach. Certified by Califonia K, which is a division of the OK.
The tillamook chedder At trader Joes is Kosher. Do a search on this site for Tillamook…Should come up
Some of the medium cheddar does have a hechscher.