Inconsistency? Sure.
Huge? I think that’s up to interpretation.
ETA: There are also many occasions when Spock says that Vulcans do not lie, but in many cases, Spock does in fact lie. In the scene in question, Spock indicates that a mind meld is a very personal thing. He is talking to McCoy, someone there is a love-hate relationship with and Van Gelder, someone he really doesn’t know. Would you tell a deep personal secret to that audience? I wouldn’t.
In the end, I don’t look at this as an inconsistency, but instead as a deepening of the character.