This is where the double standards come in.
A lot of people on the right that describe themselves as being in favour of free market economics are not really in favour of free and competitive markets at all, they are in favour of a market where they have market power.
Perfectly competitive markets mean zero supernormal profits, ie the owners of capital get nothing, other than covering their own costs, they break even. Nobody loses out, because the owners of capital have their costs covered, workers get paid a fair wage equal to the value of the product of their labour (ie the owners of capital cannot extract surplus value out of the workers, as Marx described), consumers pay a price equal to the cost of production and no more, and resources are used efficiently in society.
If you are really in favour of free markets then you have to tackle market failures like:
externalities (eg pollution) - costs that are not factored in to the market, so you have to create a market for them by forcing polluters to face the costs of their actions
market power - the ability to charge a price over cost of production
incomplete information - firms not fully disclosing information on their products to consumers
Of course to make the free market work these market failures need addressing by governments. But this is the point where a lot of the "free market" supporters will cry "tyranny of big government" because they want to preserve a position where they have a market skewed in their favour.