Barbarians aren’t even humans. How could they possibly compete with us? It’s like competing with a dog or an oyster. Worse, in fact. You can beat a dog when it is impudent to you. Or eat it. All you can do with barbarians is run them through with a sword. Boring, boring, boring. What’s next, allowing slaves to compete? What has happened Greece?
Hmm... now hear me out, what if - and now I'm just throwing ideas around - we make an arena for the barbarians to compete in with wild animals and we watch..? It could be circular arena, hmm yes. Then I can still compete naked and all oiled up (just avoid being grappled while boxing, same goes for the other man!) with all my favourite sworn enemies from mighty Greece!
Outrageous! What will they think of next? I guess we'll just let all the competitors place curses on eachother too then? The statues of Zeus are there for a reason, people!
That attitude will soon have you pay for the next statue of Zeus, mister.
(Adding: there's a row of Statues of Zeus near the Olympic stadium, with plaques describing why they were placed. The idea was that these would be bought with the fines placed on cheaters. One common way to cheat was to have various gods and/or powers place a curse on the competition, and we have numerous records of this)
Why not? So long as it is in segregated events with oversight to ensure the spectators do not crowd. They should be allowed to show the gifts the Gods gave to them. So long as a father, or brother acts as escort to ensure that they are of proper character and to negotiate any marriage proposals.
I would not be opposed to adding horse racing, or perhaps chariot races. Leave it for a side event though. The main attraction must be the athletes, but so long as many come from afar, let them bring animals to race and bet their coins on.
As for women competing? Well... there is much said of showing the vigoriousness they can give, but only in separate events! to ask them to compete against men would be to invite undue advances that would degenerate sport into a pell-mell of bodies in sacrilegious acts.