Of course, when you have multiple full newsrooms, you care about location capabilities. I get a customized California feed (California Today) when I go to it.
"California Today" needing a location capability - I'm not sure if you're entirely serious. Why would it need to access your current location - people read local news for where they live, not where they happen to be. And whether you're in California or not is not something that changes frequently. Nor is California Today a travel guide - it has no relevance for people who happen to be in California. Do you actually know if it's based on your real time location? I doubt it. And even if it was, it doesn't have to be.
Also looking at this - https://www.nytimes.com/column/california-today - it consists of an article every other day or so? This is why they need the location data? And it doesn't look like it's a customized feed at all - seems like everyone gets the exact same feed. What data do they need to put this together? And it looks like they have a signup sheet - https://www.nytimes.com/newsletters/signup/CA - are you sure they don't automatically sign you up based on your permanent address? I mean, consider the level of location access (frequency and granularity) needed to show New York news vs California news and compare that against, say, turn-by-turn navigation.
Also I just downloaded the app and it has "Australia" as a top-level section by default (I'm in the US). Are you sure user location is used meaningfully for anything in the app?
If the president of the World Curling Federation were to publish an op-ed on how the NFL's policies and protocols were inadequate in protecting players from permanent brain injuries, would "How big is curling's global audience and revenue compared to the NFLs?" or "How many pages does the WCF policy book devote to concussion protocols?" be relevant angles of rebuttal?
It's not so much hypocrisy as the fact Google's collection and use of data is skewed towards providing better services to consumers while New York Times's (and their partners' through the site/app) collection and use of data is skewed towards monetization.
Their data collection helps them decide where to build new news bureaus and news rooms and also what content they should surface to their readers. I get a very California focused NYT vs my friends who live in NYC and London.
Also, I'm sure a chunk of their privacy policy is actually impacted by using Google as their ad service and a passthrough from Google's to them.