We've just had the same problem.
tl;dr - It seems you have to unlock the transaction period to reconcile. The danger here is that may affect reports you have already made, so you should probably talk to your [advisor/accountant/person who set the lock date]
The Xero help pages identify a similar situation here where lock dates affect allocating credits to invoices outside of the lock period.
For us, we had had a bank feed transaction dated 30th June and a supplier invoice dated 1st July. In future, I'm going to make sure we've reconciled everything before we need to lock dates for year end.
To reconcile, I had to visit General Settings > Financial Settings, at the bottom of the page are two types of lock date. I set these to a date before my unreconciled transaction (28th June), reconcile, then set them back.