Yes, it is morally wrong to take screenshots of someone's Snapchat content. But we can't call it illegal in all cases. The legality of Snapchat screenshots depends on the situation or the purpose for which the screenshot is being taken.
Suppose the purpose is to show minors exploitation or people's extortion (taking an image of the other person without their consent and threatening them to fulfill your demands).
If someone is planning to do so, then he might prepare himself for getting banned by Snapchat. It will also result in the deactivation of your content for violating Snapchat's privacy.