First of all one must understand the definition of Animal rennet. Also this ruling is according to the Hanafi school of thought and is as follows;

The lawfulness of rennet does not depend on the slaughterer being a Muslim or non-Muslim, in fact it depends upon whether there is life in it or not. The circulation of blood in an organ is the cause of life. No blood flows through rennet; therefore rennet is not a living thing. Therefore, it cannot 'die' and it is thus permissible to consume rennet like dairy products.

Therefore whether the animal is slaughtered according to the Halal method or bolted the Rennet is permissible to eat. However the exception to this rule is that rennet produced from Pig is Haram and definitely unlawful. Therefore, one must ascertain whether the rennet used is not derived from pig. If it is not then it is permissible to eat.

However, where there is doubt (as is in this case between the four Madhabs) then one must err on the side of caution as children may not understand the difference between rennet and fat and may conclude that animal fat is also Halal and this is certainly not the case.