Government interference in business doesn't seem to me to be a particularly conservative position.
Depends what you mean.
You can't have business without government interference. It's government interference that allows us to have a system of private property, and the legal personality that allows large companies to be formed with many owners and the ability to operate in a large scale way over the long term.
Copyrights and trademarks are government intervention, as are the police to stop shoplifters and the court system to solve disputes. And competition law, corporate finance reporting law etc.
Being conservative is about having a minimum of this to protect people from abuse of market power while allowing markets to be as free as possible.
For example if you don't have copyright, then you don't have a way to guarantee monetising creativity - and if you don't have that, then you get less stuff created - because the creators have nothing to live on. This applies to films, music, books, software, design, research and many other areas. So it's a proper concern of government to poke its nose in here. The question is, how much?