Yes, we should boycott them, as in this 'neo-liberal' capitalist world the freedom to choose what you buy is just about the only freedom the individual has left.
I have never bought anything sold by Nike, Oakley or Trek (or Sram come to that) because of the links to Armstrong, and also because I don't agree with the model of capitalism that such companies follow. That is, outsource your production to low-wage economies where the population is practically enslaved in order to better serve the corporate interests that want to exploit their labour, then use the power of 'marketing' (including using people like Armstrong) to raise the perceived value of the product as high as the market will bear, then sit back whilst the profits flow in, profits that largely end up in the pockets of the already super-wealthy. Hence the situation were companies like Nike can have sports shirts made for literally a few cents each, and yet sell then for $50.
Unfortunately, it is getting difficult to choose to buy from companies that still have a sense of social responsibility, who support jobs in the home market and so forth. Far too many 'manufacturers' these days are simply marketing and design companies, having all their products made in low-wage economies, even as they draw on the image of traditional home-based manufacture. Companies who resist this model, such as Campagnolo, are liable to be labelled as being 'arrogant' in their assumption that more traditional models of production are still viable. For example, see
http://www.bicycling.com/news/featured-stories/italian-job
In many ways companies like Nike and Armstrong are perfect mirror image of one another. Corporate power wants to see a world where everyone views individualistic, hierarchical, inequitable, amoral 'To the winner the spoils', 'Dog eat dog', 'Look after number one' capitalism, where the only real winners are the '1%', as being the only game in town. Hyper-competitive sports people like Armstrong provide the perfect role model for such a system.
As the excellent documentary film
The Corporation points out, following the US model, companies are legally viewed as being persons. However, the typical behaviour of corporations would have them labelled as sociopaths or even psychopaths if they were persons. Again Armstrong offers an appropriate model.
I think that in many ways the world is sinking into a new form of totalitarianism based on unaccountable corporate power. Huge attempts have been made to brainwash people into thinking that 'Big government' is the real problem, 'restricting individual freedoms' and stifling the so-called 'free market'. In reality governments are at least democratically accountable and can act to protect the individual from exploitation by more powerful interests, protecting workers rights and safety, protecting the environment and so forth. Corporate interests naturally want to act without restraint, that is have totalitarian power, and so try to portray 'governments', 'the state' and collectivism in general as being a 'Road to serfdom' to use von Hayek's famous phrase. In reality the opposite is true and, as the financial crisis shows, the 'so-called 'free market' doesn't actually work in any case.
So-called 'libertarianism' might have a superficial attraction to some, but the only real 'liberty' it ultimately supports is that of corporate power. I have noticed that supporters of 'libertarianism' are fond of quoting from George Orwell's review of von Hayek's book, where he agrees that collectivism can give a "
tyrannical minority such powers as the Spanish Inquisitors never dreamed of". (My emphasis). However, they always omit Orwell's conclusion that a "return to 'free' competition means for the great mass of people a tyranny probably worse, because more irresponsible, than that of the state".
Anyhow, yes let's boycott the likes of Nike, as I said the freedom to choose what you buy is just about the only freedom the individual has left. However, a similar ethical stance needs to be taken in the case of everything we buy.
Oh, and if you work in advertising or marketing, kill yourself now.
http://www.youtube.com/watch?v=gDW_Hj2K0wo