I have a more radical approach to that : I discard any opinion I see in a press article (that is, most of it, usually), and only focus on new facts the article brings.
I don't mean any disrespect for journalists and I'm deeply thankful for their work (I even considered becoming one, as a kid), but I don't care for their opinion. I did once, before the internet, because opinions were valuable, as the only ones you were exposed to were family's and friends'.
But today, the internet is a massive opinion building/sharing machine. The last thing we need is the press to do it as well, instead it must be the place where we can expect to find facts and fact checking. I don't have any problem with random people sharing their opinion either - it's cool we can do it - but now I expect more from the press.
Now, I'm well aware solving the native ad problem does not solve the real problem : press has hard time keeping afloat. My usual suggestion about that is for browsers to include means for micro-payment (be it using google pay, cryptocurrencies, apple pay, whatever pay, a new standard, I don't care). The main problem with paywalls to me is that they expect users to subscribe for monthly subscriptions, renewed until they're manually cancelled. This is not how people consume news anymore. They come to an article because of its content, they wish to see that content, they don't want to see other articles. We need to allow people to quickly pay a small fee to see a single article, without all the hassle of using a credit card.