Apart from some online-only businesses, pretty much every business it cutting back at this point. Ads are one of the first ones to go. Esp. with the whole travel industry cutting by nearly 100%. Airlines, hotels and cruise ships spend a ton on ads and there's no point of running ads for them at this point.
Ad shows up with an ironic twist in a Coronavirus article >> somebody screenshots and posts to reddit >> instant front page >> even more free advertising but somebody calls the CEO who tells his subordinates to find somebody to yell at
For regular run of site ad buys, you're right. And a lot of CMS and ad systems come with a way to flag content as sensitive. For a small ad buy, nobody cares that much.
For big campaigns - bread and butter for print and web - different story. These are carefully designed in-your-face takeover ads and the brands care much more how they're presented.
The bigger problem is ad sales for newspapers is usually just AdSense backfill or national sales from the parent company. The former is just beer money unless your publication is NYT size, the latter is drying up because there's nobody to sell to!
Think this post is being slightly downvoted, but it is the reason according to multiple contacts in the industry. Even the ad spend which is out there is explicitly blocking COVID content for their ads.