"Please tell me this is not a huge issue."
Okay. It isn't a huge issue. The caution you mention has nothing (direct) to do with your collet die, only that any neck sized cases from other rifles may not fit into your rifle. But, your bulk (virgin) brass will be fine, at least initially.
No matter what neck sizer you use or what cases you use, you will need to FL size from time to time anyway so, yes, an FL is in your list of things to get.