I'm very much for accountability, although I fail to see exactly how it is relevant to this issue. Nevertheless, one could retort, without much of a stretch, or none at all, that if you need to store enough PII about your readers for GDPR to become a really hard issue to solve even with a ~2-year headstart, you either:

1) Weren't doing a very good job with your political reporting, and didn't know about it.

2) You are storing way too much information about your users for a newspaper to store.

3) You use deprivation of news to a particular group of people to try to influence them, or others to aid in your goals, whatever they might be.

4) You don't have that much money, and can't afford the changes necessary.

In my opinion, of these, only 4 is really acceptable for a newspaper, as news at its core is about trust, integrity and dialogue. Each of which none of the other answers leaves untainted.

... but I believe I don't even need to make the argument, because time and the growing distrust of how companies handle their sometimes very private and sensitive information don't care about arguments, it will simply make the things it cares about happen, given time, and the opportunity to be heard.