While that would be a good thing to get clarification about, the question has no bearing on the True Polymorph issue being discussed -- as noted, since Half-Orc is in the Player's Handbook, it is always available as a character creation option, since the PH is always allowed. If the PC were True Polymorphed into a race that isn't in its 'PH+1' options, such as a PH+SCAG bladesinger Polymorphed into a hobgoblin from Volo's Guide, then the question would be more directly applicable.
The question being posited by a Half-Orc bladesinger is this: is a non-elf bladesinger or non-dwarf battlerager unplayable, or is it simply not allowed to continue advancing in that class? It should be noted, though, that if you are reincarnated as a non-elf or non-dwarf, you are not prevented from continuing to advance as a bladesinger or battlerager -- the FAQ explicitly allows for non-elf bladesingers via reincarnation, so I could see an argument justifying that True Polymorph, as another spell that can change a PC's race, would also not prevent the character from continuing to be a bladesinger. On the other hand, the rule in 5e is generally 'a game effect states what it does, and if it doesn't state something, it doesn't do that something' -- by this reasoning, the guidance for Reincarnate does not necessarily apply to True Polymorph, since they are different spells with different game effects. (As another example of the distinction between the spells -- the race of a character that is subjected to True Polymorph is chosen by the caster, while the race of a character that is subjected to Reincarnate is determined randomly by the DM. There is much less potential for abuse with the latter spell, so it makes sense that the rules related to preventing its abuse would be less strict.)
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Pauper
