In most cases, it depends on the platform's terms of service. If the platform allows for privacy settings or modes that enable a certain level of anonymity while viewing stories, then it is legal as long as you are following their rules.
It depends on the method. If you are using a legitimate feature provided by the platform to protect your privacy while viewing stories, then it is legal. For example, if a platform has a privacy - enhanced viewing mode that doesn't disclose your identity more than necessary, that's okay. However, if you are using hacks or third - party apps that violate the platform's terms of service to watch anonymously, it is likely illegal.
To watch stories anonymously, you could consider using specialized privacy browsers or apps that are designed to protect your identity. However, make sure you understand the terms and conditions and the limitations of such tools.
One way to watch stories anonymously is by using private browsing modes in your browser. However, this doesn't guarantee complete anonymity. Another option could be accessing through anonymous proxy servers, but they might not be reliable.