"I thought gender was being removed from succession of the Crown. Would that not make Anne second in line?"

No on two fronts! Firstly the plan is to change the law specifically worded in regard to the descendents of Charles. Hence the first ones to be effected would be his grand-children as both his children are male anyway. Secondly even if the law immediately changed for all exisitng royals shaking up the current line then Anne still wouldn't be second in line. The oldest sibling next to Charles would have been second in line until Charles himself had offspring. Disregarding anyone's sex then Anne would only be 4th in line at the moment and would be pushed down to 5th on the birth of this baby!