https://grammarist.com/words/ilk/#:~:text=It's%20neutral.,a%....
Also, note that all of the negative examples are politics related. If a politician reads the word 'ilk', it is going to be interpreted negatively. It might be the case that ilk does "always mean" a negative connotation in politics.
You could change 'ilk' to 'friends', and keep the same meaning with very little negative connotation. There is still a slight negative connotation here, in the political arena, but it's a very vague shade, and I like it here.
"Altman and his ilk try to claim that..." is a negative phrase because "ilk" is negative, but also because "try to claim" is invalidating and dismissive. So this has elements or notes of an emotional attack, rather than a purely rational argument. If someone is already leaning towards Altman's side, then this will feel like an attack and like you are the enemy.
"Altman claims that..." removes all connotation and sticks to just the facts.