I think contributions to StackExchange constitute a valuable thing for an academic to do. In many cases such contributions are directly related to the aims of an academic department: community engagement, building new knowledge, etc. This is particularly clear for sites that directly align with a particular academic discipline (e.g., mathematics, statistics, psychology).
However, many people in academia have not heard of StackExchange. They often won't have heard about the reputation system. They may not be aware of the high quality content that often appears.
Thus, as an academic, how should you share your achievements on the StackExchange network in contexts where how your performance is evaluated has material consequences? (e.g., a CV, job interview, grant application context, promotion context)
The StackExchange point system is not a metric for anything other than "how much we trust you to use the site correctly". The idea exists to balance the needs of a public/open/crowdsourced/self-moderating Q&A system, with protection from internet trolls and defacement. The authors of SE even said themselves that "reputation was useless," and not a proxy for the value someone brings to the site.
For example, some people like Brian Tompsett rack up huge amounts of points by editing posts with minor spelling corrections, and thereafter gets a small fraction of reputation points for ever upvote the original post gets. This is NOT to say Brian's work is meaningless though - it absolutely is not - but you can't just look at a score and directly convert it into value to the community since there are so many different ways to gain rep.
I am myself a pretty good example of this. Recently I made a question regarding my poor working conditions which gained the most number of views for a question on the site to date. Probably because many people felt sympathetic to my circumstances, it gained a large number of upvotes too. I am under no illusion however, that my question and thus my account has anything like the value to the community that my rep score indicates. The large number of upvotes however, gave me the psychological support i needed to tell my boss that my working conditions are unfair, despite what he claims, and now everything on my end is much much better - so ironically, it was the upvotes themselves that had value, not the question.
There are also numerous answers that contain "hard truths" that get heavily down-voted not because they are inaccurate, but because people just don't like what they are reading - despite it having considerable value. People who play devil's advocate get hit by this the hardest.
So you see there is only a weak correlation between between rep and value to the site - and that is by design. Anyone who would know what to do with your rep score if seen on a CV would likely know this too, so if you do go on to put your academia.SE details on your CV, make sure to highlight why you like helping people, whether you like to ask good/insightful questions or answer technical/demanding questions with research, etc etc. Don't make any reference to rep, because the person reading the review won't be impressed - particularly if their rep score is lower or much higher than yours ;)