Does Phyrexian mana count as colored mana for color identity in Commander?

There are two separate questions here that are often confused: (1) what color identity does a Phyrexian mana symbol grant a card, and (2) what kind of mana do you spend when paying a Phyrexian cost? These have different answers.

For color identity, CR rule 903.4 states that a card's color identity includes the colors of any mana symbols in its rules text, including in ability costs. A Phyrexian mana symbol such as {W/P} is a white mana symbol for the purposes of color identity (CR 202.2c). So a card like Gitaxian Probe has a blue color identity because its cost contains {U/P}, even though you can pay it with 2 life.

For paying the cost, when you choose to pay 2 life instead of mana for a Phyrexian symbol, you are not producing or spending any mana at all — colored or otherwise (CR 107.4f). The payment of life is simply an alternative to paying the colored mana cost.

Concrete example: Birthing Pod has {3}{G/P} in its mana cost. Its Commander color identity is green because of the {G/P} symbol. You cannot include it in a colorless or non-green Commander deck. However, when casting it, you may pay 2 life in place of {G}, spending only {3} colorless mana if you wish.

In summary: Phyrexian symbols do contribute their color to a card's identity under Commander rules, but paying life to satisfy that symbol does not count as paying colored mana.