Generally this would be fine since you can interline these two tickets for sure upon check-in. And I'm almost certain CX wouldn't charge you if you missed the flight flying in on oneworld carrier.

My concern as midlevels mentioned would be the refusal to interline since you're under the 90 minute mark. I'd call BA and reconfirm this connection time and their policy.

Normally you can get a refund / free change if the schedule change impacts you negatively so if you want to change the flights I would believe they'd let you.