I don't think it's just the word - I think it's the combination of the word and the usage.
If your "GitStart" startup was intended to help "unpleasant, silly, incompetent, annoying, senile, elderly or childish person[s]" to start doing something, I think you'd have no problems from a trademark perspective.
If your "GitStart" startup is to help people start doing something with Git, the (trademark-ed) source code management system, then you might be in trouble.
If GitHub was granted an exclusive word trademark, then copying some or all of it should result in an accepted opposition by the USPTO. It doesn't matter if the offender company is in another segment, since GitHub is a notorious trademark (i.e. if you try to trademark MacHair for a hair salon, you will get sued by Apple and/or Macdonald's).
However, I don't think it's the case, since the word GIT has been used by other entities long before GitHub came to be. Otherwise, we wouldn't have GitLab, for instance.
If your "GitStart" startup was intended to help "unpleasant, silly, incompetent, annoying, senile, elderly or childish person[s]" to start doing something, I think you'd have no problems from a trademark perspective.
If your "GitStart" startup is to help people start doing something with Git, the (trademark-ed) source code management system, then you might be in trouble.
IANAL.