Depends. The more values oriented culture warrior types tend to be baby boomers stretching back to the formation of the
New Left. The kind you see today online are more secular and not so much values based. They're the ones preaching a more civic minded reform (see their usage of the words "systemic" and "institutional" to describe sexism and racism). These are far more likely to be millennials.
The typical kind of SJW that we think of tends to be more of the latter so yes; those ones are generally millennials.