Because they've always marketed astronauts as paragons of virtue and skill, and something that any parent would be happy to have their child strive for. As soon as any one of them behaves in a way that any of those parents may disagree with, they're dirtying that public image in the eyes of some.

NASA is obviously acutely aware of how precarious their funding often is, so walks a fine line in an attempt to make the only critique against them purely budgetary and not political. Like it or not, showing too much personality allows one side or the other to start positioning you as a piece for or against their agenda (and of course the other side will take the opposite stance), making it a political issue even if it's ridiculous to think of it as so.

>attempt to make the only critique against them purely budgetary and not political.they're dirtying that public image in the eyes of some.

Yet they drew plenty of non-budgetary criticism for rescinding her internship, so it doesn't seem like that worked out for them.