https://breadwallet.com/blog/what-fork-means-breadwallet/

In the case of a fork, breadwallet will continue to connect to the chain that is the most popular amongst miners. You will not see your balance on the less-popular chain.

We expect the less-popular chain to quickly lose support and be abandoned, which is why we have not invested a lot of resources into adding the capability to interact with both chains separately.

They will also not allow accessing your current coins on the current Bitcoin network, unless BU implements replay protection:

In order for breadwallet users to be able to send and receive funds on the chain of their choosing, a feature called “replay protection” needs to be designed.

It should be the other way around – if BU wants to be supported, they must add replay-attack protection. Preventing people from accessing their Core coins until BU implements replay-attack protection is a sure way to ensure that BU never implements replay-attack protection. Insanity.

Bitrated (disclaimer: I'm the founder), BitGo and Bitonic got it right. It is not responsible to support BU unless they implement the hardfork-related safety measures (they're the ones initiating the fork, while Core stays put).

The only rational thing to do without these basic safety measures is to simply ignore BU.

Breadwallet, can you please stop this insanity, take a clear stand against technically irresponsible hardforks, and ensure that your users don't unknowingly get forced onto a new network that they never agreed to?