In the context of this talk, APN means "Apple Push Network", I think. The concern is that even if the service doesn't ask for a phone number directly, it does still have an APN or GCM/FCM push token. Through the push provider, that token can probably be linked to the user's phone number.

> With unlocked smartphones, it is possible to remove the SIM card, clear any APN settings and access WiFi.

If you're willing to do all that, I suppose getting some free VoIP number for registering with Signal (e.g. through Textnow) won't be too much of a hassle?