The new rule will take effect in Apple Stores and Apple Authorized Service Providers. While Apple previously disallowed this, currently they will repair phones with non-Apple batteries, even when the batteries are the root of the problem.
In the past, Apple denied any repairs if an iPhone had an-off brand replacement battery even if the repair issue had nothing to do with the battery. In June 2018, Australian officials fined Apple $9 million (AUD) about ($6.7 million USD) for not offering repairs to customers being affected by a glitch caused by a third party repair issue over the policy.
Now, Apple will repair with third-party batteries even when batteries are the roof of the problem. they'll replace your janky battery with a nice Apple one, for a fee and how kind.
Apple changed a similar policy in 2017 regarding third-party screen replacements. However, according to MacRumors, it still won't touch phones with replacement "logic boards, enclosures, microphones, Lightning connectors, headphone jacks, volume and sleep or wake buttons, TrueDepth sensor arrays."
Tech company have faced increasing criticism over how tightly they hold the reins when it comes to repairing their devices. Some feel that consumers should have the "right to repair" the devices they bought and paid for, however they wish — and that companies like Apple should enable that.
Right-to-Repair legislation, which would codify this stance in law, is currently wending its way through multiple state legislatures; California became the 18th state to introduce a bill like this in March 2018.
Apple has been lobbying against these efforts. So perhaps the new repair policy is a way to show that they're willing to have a more lenient and open stance about device repair, as long as their customers always come back to the mother-ship.