Do graduate committees in math decide to not take students based on lack of knowledge of specific topics?
Mathematics as a whole is very broad. It has been about a hundred years since any individual could say s/he knew all of it. Mathematicians are specialists - often extremely so. So, if you are working in a different area, having little knowledge of an unrelated one is not considered much of a disadvantage. 

On the other hand, it is possible in the US to gain admission to doctoral programs, even very good ones, with only an undergraduate education. In the US the undergraduate education is very broad with only a little specialization. A math major also studies history and philosophy for example. So, the undergraduate math education, while, itself broad, can't cover everything. 

However, if you are interviewed for a doctoral position the interviewers will decide on the questions. You need to make sensible answers, of course, but most interviewers will be looking for general math ability, not expertise in everything. That would be different, of course, if you are interviewed by a potential advisor who will want to know about you background in a particular specialty. 

But from your description, your lack of specific knowledge in a few areas isn't likely to be a handicap. However, the competition for any slot will be intense at the level for which you aim. Nothing is guaranteed.