For reference to where this is stated:
- p. 6 of the core rules lists the "When to play" for Classes and Races, and it says: "These cards may be played to the table as soon as they are acquired, or at any time during your own turn."
- p. 4 of the core rules describes both character stats Race and Class, and those sections say: "You can discard a Race card at any time, even in combat[.]"
Those page numbers are valid for
Munchkin and
Munchkin Deluxe.