They just don't seem to really understand what we've been saying.
"For online survey research, is it problematic when the status or legitimacy of the quantitative response is undermined by an explanation that challenges the premise of the question? For example, criticizing a statement because of an objection to the use of the word gender (rather than sex) rather than simply responding to it on its own terms."
Yes, it's 'problematic', because substituting the word gender for sex in a survey like this isn't just playing semantic games. It's at the heart of the issue. It's impossible to respond to a question 'on its own terms' when that means accepting false premises as true.
Survey response: "Male and female are biological sexes. They are not genders. There are two sexes. (Intersex people make no difference here as they are outliers which do not disprove the existence of sexual dimorphism and certainly don’t demonstrate that sex is a spectrum"
Researcher's commentary: "The problematic erasure of people with intersex variations in the second response (above) also demonstrates a highly ‘endosexist’ (non-intersex) perspective."
How exactly can you interpret 'people with intersex conditions don't demonstrate that sex is a spectrum' as 'erasing intersex people' unless you've already been subjected to ideological capture? Surely 'erasure', if you have to use the term, would be saying that intersex conditions don't exist - which is not what the respondent said at all.
"At first glance these figures appear to suggest that a large percentage of respondents were supportive of the view that gender is not binary, and that genders outside of female and male exist and are valid."
Language capture. What does it mean to be 'valid' in this context?
"While the first example here does highlight the increased receptiveness to gender as a ‘fluid concept’, the perceived fixedness of biological sex is reinforced."
Perceived? 
"The influence of biological sex in shaping people’s lived experience was evident, and persistently used as a bottom-line argument to counter any challenges to the gender binary through its placement as a central, undisputable [sic] fact."
This is the kind of nonsensical conclusion you draw about GC views when you conflate sex with gender.
As an alumna of King's I find this depressing.