Many law firms attempt to represent both insurance companies and injured people who have claims against insurance companies. Unless the insurance company is the same one in both cases, there is usually nothing illegal or impermissible about this practice.
However, there are times when a client's interests require a position to be taken about the law that is opposed by the entire insurance industry. Precedent set in one case can detrimentally affect all insurance companies with cases of that type pending. That puts a lawyer who tries to handle both sides of liability claims in a difficult position. He knows that winning the case for one injured client could hurt his insurance company clients on many, many other open cases.
That is a problem we avoid in our firm by simply refusing to represent insurance companies in cases against injured people.