I have been developing on a fork of an open-source code which had Apache MIT dual license at the time of fork.
Recently they changed their licensing to exclude commercial uses: 1. personal use for research, personal study, private entertainment, hobby projects or amateur pursuits, in each case without any anticipated commercial application; 2. use by any charitable organization, educational institution, public research organization, public safety or health organization, environmental protection organization or government institution; or 3. the number of monthly active users of the Resulting Program across all versions thereof and platforms globally do not exceed 10,000 at any time.
Is it legal for me to continue using the fork if I don't merge their latest codebase which reflects the change in license?
It doesn’t just include mechanical merging. Manually applying essentially identical changes also would be a no-no. Even just looking at changes they made to implement similar functionality on your fork (say for a small security fix) could be interpreted as requiring a license change in your fork.
IANAL, but reading about their new features and bug fixes would, IMO, be OK.