It is amazing how easy it is in the US to name your group something important sounding to trick people. The letter you quoted was so over the top and such a mismatch with actual surveys of doctors, that I decided to check on the organization you cited: https://en.wikipedia.org/wiki/Association_of_American_Physicians_and_Surgeons

The Association of American Physicians and Surgeons (AAPS) is a conservative non-profit association that promotes medical disinformation, such as HIV/AIDS denialism, the abortion-breast cancer hypothesis, vaccine and autism connections, and homosexuality reducing life expectancy. The association was founded in 1943 to oppose a government attempt to nationalize health care. The group has included notable members, including American Republican politicians Ron Paul, Rand Paul, and Tom Price.

In 1966, The New York Times described AAPS as an "ultra-right-wing ... political-economic rather than a medical group", and said some of its leaders were members of the John Birch Society.[5]

The group was reported to have about 4,000 members in 2005, and 5,000 in 2014.[8][9][10]

Wow, such a big group... Yes, when getting medical advice, makes a lot of sense to listen to the head of an openly political medical group of ~5000 people instead of a nonpartisan survey of all doctors. A group of 5000 is very small in the US:

As of 2018, there were over 985,000 practicing physicians in the United States
https://en.wikipedia.org/wiki/Physicians_in_the_United_States#:~:text=As%20of%202018%2C%20there%20were,licensed%20in%20a%20medical%20specialty.

I now suspect this is why you are coming to such bad conclusions about the risks of covid vaccinations: it seems you are prioritizing your belief in politically-biased sources rather than scientific ones.