Newspapers publish opinions for the same reason that they publish comic strips: people want to read them. Readers seek them out. Newspapers are a business and have to give their customers what they want. The problematic aspect here is that the current business owner, Jeff Bezos, has a conflict of interest. Bezos is making a bad business decision for The Washington Post, sacrificing it and losing readers for the sake…
WaPo's business is catering to D.C. professionals. The nature of the country's electoral politics is that roughly half of those are going to be batting for each side. It's a good business decision not to seem like you're rooting for one side or the other.