Change the oil in the differential?

With a vehicle that age I would also change all belts/hoses/fluids period. You eliminate or reduce anyway many future problems. Tire check age/condition.

15 years old time to change it.
Replace with synthetic and will be the last time you will need it done.
Unless you keep it for another 15 + years.

Yes, change it as when it gets foamy it does not do the job it should!

I'm sure there are a lot of vehicles on the road that have never had the oil changed in the differential. But, that doesn't mean you should never change it.
It's good Preventative Maintenance.
And, it's not difficult or expensive so, I doubt your mechanic is doing it to get more money from you.
Did you check the owners manual? That should have the schedule for changing fluids.

I do in all my vehicles.