You should care at least as much for the security of your e-mail account, especially if it was used to register your Twitter or Facebook accounts. A compromised email account opens op new ways for the bad guys to get into your other accounts. This advice can be extended to general online activity, not just social networks, and most importantly not just Twitter. The bug in Edge s auto-translate could have let remote attackers pull off RCE on any foreign-language website just by sending a message with an XSS payload.
Source: https://threatpost.com/slideshowsecure-your-e-mail/89309/