Can I export audience User IDs?

Facebook generates separate user IDs for every App that is connected to your Page. This means that the user IDs that ManyChat gets from Facebook are only useful for us and not for any other app.

However, you will be able to get your own user IDs if you connect your app to your page, send a broadcast through ManyChat and then listen for the Echo Callback which will contain all the user IDs that are specific to your app.
This way you have control over your audience and not locked-in into any service.