iOS 9.1 is safe to upgrade, if you are already on 7 or 7.0.3. But, if you are using iOS 6.1.3 jailbreak, then avoid this update until the iOS 9.1 jailbreak tool doesn’t ready.
iOS 9.1 has been released publicly by Apple. After each update, thousands users look jailbreak for that release. There was a huge spike in the jailbreak users who were looking iOS 9.1 jailbreak and they couldn’t get what they wanted except just a tweet from MuscleNerd, a jailbreak team member.
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Just after iOS 9.1 released, Evad3rs team member, MuscleNerd, has tweeted and said that 8.1 is jailbreak safe and you can upgrade to it, only if you are already on iOS 9 or newer firmware.
However, you should avoid iOS 9.1 to upgrade, if you are already using iOS 6.1.3 evasiOn JB tool. Its better to wait for 8.1 jailbreak from official JB team.
Meanwhile, Evad3rs itself has updated their blog and warned users who are looking official iOS 9.1 jailbreak software evasiOn tool that don’t download any faker JB tool from any website, because jailbreak for iOS 9.1 not yet.