Sealing both is fine. No harm at all.
It is typical to seal the inside only, in most cases. That keeps the sealant hidden. If it weeps, it usually just means a pin-spot was missed.
“I think that when the lies are all told and forgot the truth will be there yet. It dont move about from place to place and it dont change from time to time. You cant corrupt it any more than you can salt salt.” - Cormac McCarthy