Where did "Open in Safari" go?
One of the recent version update changelogs for Tweetbot states they made a change to the share sheet, which may in turn have caused a bug that is preventing Safari from showing up. This would best be reported to the developer of the app.

In iOS 8.x, a developer basically advertises "I have this type of data to be shared, what apps can share it?" The system responds with a list of apps that are capable of receiving that type of data. (Types can include text, a web URL, images, and so forth.) Depending on what type of data Tweetbot is advertising, it may not be compatible with what Safari says it can receive - Tweetbot might be advertising the URL in plain text format, whereas Safari might only be able to receive the URL specifically formatted as a URL.