Is it safe to delete the built in apps on my iPhone that give me the option to delete them?

It affects functionality in that you won't have the functions of the apps you delete. Also, if you have an Apple Watch, deleting the app from the phone will also delete its functionality from the watch. But, it won't hurt anything and you can always add the apps back if you want to.

If any app, built in or not, provides an option to delete it from your iPhone, then you can do so without worrying about functionality or security issues.

Axel F.