I'll add the old "me too" vote to this one for the vault page opening.
Numerous computers ... my own desktops and laptops, friend's, family ... the vault page opens in both Firefox AND Chrome upon startup. That setting in the extension is turned off, so this shouldn't be happening. I should just get prompted to login to LastPass. I do not. As others have said, it is EXTREMELY frustrating that this issue has been going on for MONTHS without a resolution.
Regarding Chrome and Firefox not sharing the login session, I had to go into the Chrome extension and Account Options -> About LastPass. Then I had to click the Enable Native Messaging button. After a Chrome restart, it now appears to pick up the login from Firefox and vice-versa.