Yes, the Mutate cost is an alternative cost. No, you can't pay WUBRG for Mutate through Jodah, and that is because both are alternative costs.
A spell's mana cost is only what's printed in the upper right corner of the card, nothing else. In particular, an alternative cost is not a mana cost.
202.1. A card’s mana cost is indicated by mana symbols near the top of the card. (See rule 107.4.) On most cards, these symbols are printed in the upper right corner.
The alternative cost granted by Jodah is independent of the Mutate alternative cost; alternative costs are an alternative only to the spell's mana cost, not to other alternative costs. You have to choose between paying the mana cost or one of the alternative costs. Only the associated effects, if any, of the cost you chose to pay actually happen.
118.9. Some spells have alternative costs. An alternative cost is a cost listed in a spell’s text, or applied to it from another effect, that its controller may pay rather than paying the spell’s mana cost. [..]
601.2b [..] If the spell has alternative or additional costs that will be paid as it’s being cast such as buyback or kicker costs (see rules 118.8 and 118.9), the player announces their intentions to pay any or all of those costs (see rule 601.2f). A player can’t apply two alternative methods of casting or two alternative costs to a single spell. [..]
So if you control Jodah and cast Nethroi, you can choose between paying Nethroi's mana cost of 2WBG, Jodah's alternative cost of WUBRG, or Nethroi's Mutate alternative cost of 4(G/W)BB. You get to Mutate if and only if you paid the Mutate cost.