I think LessWrong is sufficiently seperated from SIAI - most LessWrong members are not involved at all with SIAI, and many SIAI members/advisors/whatchamacallits don't post on LessWrong (I think).
It's not detached yet - it's still to a large degree about SIAI-related interests that are not related to the (excellent) tagline "a community blog devoted to the art of refining human rationality".
There are plenty of front-page promoted posts that are essentially advertising for SIAI, reasons why you should donate all you can spare to SIAI or how-tos on ways for readers to make money to donate to SIAI. Which I can live with - it's no more annoying than the banners on Wikipedia at the end of each year, and it takes money to keep the lights on - but it's not obviously on-mission (taking the tagline at face value).
I think that one day LW should be more independent of SIAI, but it's not a problem that it isn't yet and it can happen at its own pace.
I was recently thinking about the possibility that someone with a lot of influence might at some point try to damage LessWrong and the SIAI and what preemptive measures one could take to counter it.
If you believe that the SIAI does the most important work in the universe and if you believe that LessWrong serves the purpose of educating people to become more rational and subsequently understand the importance of trying to mitigate risks from AI, then you should care about public relations, you should try to communicate your honesty and well-intentioned motives as effectively as possible.
Public relations are very important because a good reputation is necessary to do the following:
An attack scenario
First one has to identify characteristics that could potentially be used to cast a damaging light on this community. Here the most obvious possibility seems to be to portray the SIAI, together with LessWrong, as a cult.
After some superficial examination an outsider might conclude the following about this community:
Most of this might sound wrong to the well-read LessWrong reader. But how would those points be received by mediocre rationalists who don't know what you know, especially if eloquently summarized by a famous and respected person?
Preemptive measures
How one might counter such conclusions:
So what do you think needs improvement and what would you do about it?