I could say something similar to the Mormon as I could to the Muslim as both make a similar claim about the truth being corrupted that a new revelation was necessary.
This is not a problem that Christians generally have. Even those who have adopted a form of extra-Scripture traditionalism of their own do not maintain that the Gospel and Hebrew Scriptures has been either disrupted or is somehow fundamentally altered.
As for traditions, there is a difference between Scripture and traditions that have been added to it, often long after the fact. Indeed, to this day there is a whole branch of Judaism known as the Karaites that dispute the propriety of writing down and subsequently elevating the traditions.
The kararites started in ~750 CE with the sponsorship of the Muslim Caliphate to make it easier to convert ignorant Jews to Islam.
Hardly a reliable group.
The new seeks to replace the old. The thrust is the same regardless of the claim on the “old.” Claim it’s corrupted, claim it’s not-fully-revealed (claim some have scales over their eyes,) but no one disputes the veracity of the Jewish Bible. Everything else is addenda, is it not?