Politics is a tough old game and not for the thin-skinned or faint hearted. As early as the 17th and 18th century political satirists have been plying their trade and many politicians (almost always men) have been mercilessly lampooned since those early days.
Anyone who gets into politics know both what they say and their physical appearance will come under the closest scrutiny and they have to be prepared for it. This applies to both men and women. And the more successful they are the more flak they are likely to take, especially from people who do not agree will their political views. And nobody would argue that Nicola Sturgeon is a very successful politician.