In my opinion, if you boldly compare yourself to a dog and the only difference between you and that dog is lipstick, then you have lost the right to cry sexism at a veiled reference to a pig lobbed in your direction.
Actual meaning of the aphorism "Lipstick on a Pig":
A term used by many, generally in reference to someone who may be trying to make something look appealing or attractive when it quite clearly isn't.
If you don't want to be treated differently, then you can't cry foul whenever you've perceived an insult hurled at you related to your gender. You have to become impervious to your gender in fact. Not in your ownership of it, but in your defense of it. You have to own your gender and you have to own your responsibility to removing people's perceptions of it in their associations with you and only you. I can do nothing to force someone else to think well of other women. I can only change their opinion of me and then hope that this positively impacts their next association. If I forced every man I work with to respect me based on my being a woman, then I have done myself a disservice and gained nothing. If I aim to be respected among my peers (both women and men) through hard work and fair-mindedness, then I have been successful in removing sexist barriers.
If someone says something crummy about me and it's related to my gender, who cares? What if they said something crummy about me and it wasn't related to my gender? Would it bother me more or less? Just because they say something crummy about me at all, does that make them sexist or does it just mean that this person doesn't think well of me? Does every man have to like me because I'm a woman? If another woman says something crummy about me, does that then make her sexist as well? Where do we draw the line between sexism and the process of making a point? Is a hundred year old comparison off limits to this campaign because a woman is involved now? Is this what we want as women? People tip toeing around our gender for fear of being labeled sexist over something that isn't even remotely sexist.
Is this the definition of progress that we seek?