I'd tend to agree with Janus's initial comment - to me, moonlighting very often implies working "unofficially" (not necessarily properly regulated, or paying the proper taxes). But in my own field (software development) companies often take a dim view of it for a very different reason. At least one company explicitly banned it in my Contract of Employment, which at the time I thought odd.
I asked my manager why, and he explained that even though I was only "officially" working for the company during office hours, it was quite likely I'd be productively mulling things over at other times. It was a long time ago, but I'm pretty certain he even went so far as to say I could be subconsciously solving work-related problems while doing other things (including dreaming! :)
At the time I thought that was taking things a bit far, but in later life as an independent consultant designing and implementing systems for a range of clients (where I might well "re-sell" the same system after the first client had paid for the development) I found there was a great deal of truth in the concept. At a certain level, the employer is paying for the "whole man", not just worked hours.
That's why I always rejected offers from clients to take me on full-time. Even though they were always offering me more money than I was making at the time, I valued the "future asset" of my "blue-sky" unpaid-for tinkerings more than their here-and-now pay rises.
In short, there are several reasons why "moonlighting" might be seen as undesirable (the worker himself often resents having to do it, since it implies he's not being paid enough in his "day job"). Doubtless many people think it's "neutral", but the few who think it's "positive" (because it shows diligent commitment to the protestant work ethic, duty to provide for one's family, etc.) are almost certainly outweighed by those who don't like it for one reason or another.
Having said all that, I personally think it's almost impossible to separate the connotations of the word itself from those associated with the referent. But given how often moonlighting on the side occurs in Google Books, and the undoubted surreptitious, clandestine connotations of things done on the side (extramarital affairs, for example), I would say on average it's a negative term.