No, it isn't.
Not at the moment. Firefox add-ons can only access the browser in a certain set of ways, called the API. With Firefox 57, this API was severely restricted, meaning that StartupMaster and a lot of other add-ons no longer have access to the functions they need to work. There is good justification behind these changes such as security issues, decreasing the maintenance burden and preparing the way for bigger changes in Firefox, but unfortunately it also has some serious side effects.
StartupMaster works by interrupting the startup sequence and requesting the built-in password manager to show the password prompt. The new API doesn't allow any access to the password manager and has some issues with interrupting the startup sequence as well. This makes it impossible to implement StartupMaster's functionality.
It depends on what you are using StartupMaster for. If you are trying to lock out casual users from a Firefox session, it was never a supported scenario, but answers A and C below will still work. If you would like to avoid multiple master password prompts, you can continue with any of the options.
A. Keep using the legacy API. This is especially useful if you have other add-ons that aren't compatible with Firefox 57. You can either change to Firefox ESR which will support the old API until 26 June 2018, or use Firefox Nightly and enable legacy extesions.
B. Use a third-party password manager instead of the one built into Firefox. Take a look at KeePass, Bitwarden, Passbolt, unix pass or look at the current list at the Mozilla add-ons site.
C. Encrypt your Firefox profile folder (or the entire disk) instead of using a master password. If you prefer disk encryption, you can use VeraCrypt or your platform's native encyption method (BitLocker/FileVault/LUKS). For file-level encryption, I suggest Safe for Windows/Mac or encfs for Unix-likes.
D. Live with multiple password prompts. Enter your password into the first one and press ESC for the rest.
Yes, you can. Thunderbird isn't affected by the API change.
It's difficult to tell because it's partially out of my control. It roughly depends on the status of the following three Firefox bugs:
Bug 177175: This is the original one about multiple password prompts. It could be solved by wrapping password queries in multithreading/multiprocessing locking constructs. Unfortunately this part of code is 20 years old, barely maintained and there is no consensus among Firefox developers whether to remove it completely, rewrite it or just leave it as is. Therefore no one is willing to touch it at this point.
Bug 1359182: This is about adding an API to manage master passwords. It would allow me to rewrite StartupMaster for Firefox 57+. I'm willing to write the patch adding the new API, but it needs to be triaged and approved by Mozilla first.
Bug 1361838: This would implement StartupMaster's core functionality within Firefox and expose it via a hidden preference. You would need to set up a master password yourself in Firefox preferences, then enable a special option in about:config and you would get a prompt at startup. There is a working patch, but it has been essentially rejected.