It doesn't lose credibility because their own lives are tied up in it, or even that their concerns are unfounded, it's low on credibility because the scale shifts in this pretty poor analogy.
In 1995, they moved the clock 3 minutes closer because they just generally thought not enough good stuff was happening. No particularly dire event, just a general malaise that warranted declaring 3 minutes closer to end times.
This time, they enumerate a number of specific concerns, escalating conflicts, nationalistic autocracies getting bigger, LLM induced misinformation and uncertainty, and a number of others. So now that they have more specific and more violent and more severe concerns, that suggests a more severe change, but instead, they have to move it 4 seconds.
I'm not saying they don't have a point behind the metaphor, but the metaphor itself undermines credibility. They have to budget the seconds to leave room for more bad to happen, so someone who has lived with 'a few minutes to doomsday' as the headline for decades is not inclined to regard it seriously.
I don't think anyone is arguing there are no real dangers, some may disagree with some of their concerns, but the metaphor just doesn't do the concerns justice.