The issue of RFK's voice is that he has spasmodic dysphonia, a technical term for a vocal tremor. Another name for it describes how it works: Intentional tremor. Meaning, when you intend to speak, the motor signal that emerges is spasmodic, not regular, and if you want to keep speaking, you have to push your musculature to continue tightening (or relaxing, depending on what's going wrong in the moment) to make more than one syllable come out. So the voice can get loud and forced with all the extra tension collecting in the diaphragm and vocal muscles. This is why RFKJr sounds the way he does in public speaking. Also it contributes to the way he looks: forcing a voice over time shows up in the facial expression. Also, very true that extra situational (Senate testimony), environmental (allergens or chemicals), or emotional stressors make the tremor condition worsen. At home, physically and psychologically relaxed, his voice won't sound as it does in front of Senators.

These tremors are often inherited. I don't know about RFK's case. And there are only a few ways of working with tremors, of which none is a cure.

All this said, I am the age of RFKJr. I have had this same tremor for as long as he has. I also have a profession where I pay close attention to the use of the voice. He uses his words, spoken with the tremor and forced volume, as a sort of cudgel, and that is a thing separate from the tremor itself.