I was always taught that when Isaiah 66:23 states that, “from one new moon to another and from one sabbath to another,” it simply meant, from month to month and from week to week. Isn't this correct?

Answer: Historically among Sabbatarians, Isaiah 66:23 has been most useful in showing that the Sovereign Yahuwah's true seventh-day Sabbath will continue to be kept Holy even in the New Earth by His faithful redeemed. With this said, the same specific rules that apply to the Sabbath must apply to the New Moon as well, which is also mentioned in connection with the Sabbath, giving them both specific meaning.  If the reference to the New Moon simply meant "monthly" or "from month to month" then the same would hold true for the Sabbath, which would make it's meaning dwindle to a mere "week to week", and lose its Sabbath importance.  Isaiah is defining that New Moon days, as well as seventh-day Sabbaths, will continue to be kept Holy by His faithful redeemed throughout all eternity.