As-Salaamu Alaikum wa Rahmatullah,
Thank you for your question and may Allah reward you for your diligence. With regard to Tawatur, it has the following points to be kept in mind,
1. Acceptance of tawatur is clear and must be affirmed (it is compulsory, i.e. wajib), as it touches on creedal points. This point is stressed by Imams Abu Hanifah, Muhy ud-Din, Abu Ja`far At-Tahawi and `Abdul Ghani al-Maidani, may Allah have mercy upon them, in their texts.
2. The Qur’an was transmitted through tawatur means and of course to reject that would be false, as it was mass transmitted.
3. It is for this reason that we find some of the earliest texts of creed affirming the use and acceptance of the belief in wiping over the socks, by such luminaries as Imams Ahmad ibn Hanbal, `Ubaidullah ibn Battah, Abu Hanifah, Abu Hafs An-Nasafi, Abu Ja`far at-Tahawi, and others, may Allah have mercy upon all of them.
4. This issue, although making reference to the fiqhi principle of wiping over the leather socks, is actually theological in nature as affirmation of this and other types of ahaadith of its’ kind is affirming the tawatur.
5. If someone denies the tawatur, their judgment would depend upon the following issues,
a. If the person was a new Muslim, he would be excused as he has just entered into the faith and has not learned such foundations.
b. If the person believed in the tawatur but disagreed about the content of the tawatur, this would be valid and the person would be a Muslim. An example would be the tawatur nature of the flood. Every single Muslim, laymen and theologian, believes that the flood took place and that it has been passed down unbroken.
However, there is a disagreement over whether the flood was global or not. Thus all sides affirm the tawatur fact of the flood being passed down, but in its’ content there is some disagreement, which is why there are two opinions about the flood being global or not.
And this is merely a minor difference in the branches of creed and not the foundations; therefore one is still within the fold of Islam, no matter what side they are on.
c. There are those who would deny tawatur in form and content, which is kufr without any doubt, for example the Imami Shi`a denial of the Consensus around Abu Bakr As-Siddiq as the khalifah of the Muslims and first leader after the Prophet Muhammad, peace and blessings of Allah be upon him, the fact that the Qur’an is uncreated and not created, that Allah will be seen on the Day of Judgment by believers, that only prophets and angels are infallible and many other points that are established by tawatur.
I hope that this helped and that it made sense. And with Allah is every success and help,
brother in Islam,
Al-Hajj Abu Ja`far Al-Hanbali
 Al-Fiqh ul-Akbar, pp. 4-5 of all Arabic text
 Al-Qawl ul-Fasl: Sharh ul-Fiqh il-Akbar, pp. 332-333
 Bayan us-Sunnah, creedal point #76
 Bayan us-Sunnati wal-Jama`ah: Sharh ul-`Aqidat it-Tahawiyyah, pp. 112-113
 d. 241 AH (AD 855)
 d. 387 AH (AD)
 d. 150 AH (AD 767)
 d. 513 AH (AD)
 d. 329 AH (AD )