Heather claims that A burqa ban is a symptom of racism, not secularism, nor feminism. She's completely full of shit.
She's presuming that the burqa itself has absolutely no direct material effect on women's well-being. This is obviously false. Anonymizing and desexualizing women has a direct negative effect on their well-being. Second Heather ignores the effect of non-governmental coercion: she assumes that when there's no governmental coercion on some category behavior, we can therefore conclude that any behavior in that category is an individual's uncoerced choice. This is again false. Third, she assumes that if racists affirm some statement, then affirming that statement marks one as a racist. This is a logical fallacy.
Indeed, by believing that not-quite-fully-human brown women would "voluntarily" anonymize and desexualize themselves, an action that fully-human white women would consider profoundly oppressive and fundamentally objectionable, Heather reveals her own racism.