If we go back to 1386, then we buttefly protestantism in general (much less calvinism) No, the POD must be post Luther
And I think Clavinism is outright impossible. The crown and Inquisition had too strong a hold, and by the time they lost it the time for imposed crown conversions was past.
The only way I can see a "protestant" Iberia is if some king (he would need to be a king from this TL, brought by the butterfly effect) goes the Henry IV way and Spain gets its own "anglican" religion (a french dominated papacy is the most reasonable path).
But even then this Hispanican Church would be based on the catholic one -if fact, it almost certainly would select a Pope in Exile and claim to be the real Catholic Church. The problem is, the time the papacy went against Spain's wishes (in the Henry IV divorce), Charles V sacked Rome.
As a start of the POD, make sure the Hapsburgs, catholic fanatics, do not get the throne. Make Juan survive, make Joanna barren, or whatnot. Many people on this board like the "Infante Miguel survives" POD; this allows for an Iberian Union.
Since I am suggesting a spanish anglican church, an hilarious POD would be than the Pope allows Henry IV to divorce (so he remains Catholic), Catherine and Mary return to Spain, and then either one of them eventually gets the throne and proclaims her own church. Sadly, even if we kill Joanna at the (stillborn) birth of the future Charles V, we have Queen Maria of Portugal ahead of her younger sister -and she had ten children, eight of whom reached adult age. No one expects the English Inquisition.
P.D. We cannot get a protestant Portugal either. Spain spent millions of men and doblons to fight protestantism one thousand miles away, with an enemy nation on the path. Portugal as a nation would be gone before you could say "Die filthy heretic!"