I can understand where both arguments are coming from.
On one hand, we can't just draw the same old crowd, that would be pointless. On the other, we shouldn't just hide the fact we are communist.
I think a middle ground could work, we don't simply yell 'COMMUNISM!', but we don't deny our beliefs. I think wording the homepage like:
We oppose false images of freedom. We oppose regimes in which the working man does not have a direct input in government. We oppose the use of money to influence government decisions.
We stand for the working man. We stand for his right to dominate the political world. The working class make up the majority of the population. It should be him dictating the terms to the politicians.