Translation:The working part of the men does not think that it is a good idea.
I would actually argue that the grammar makes sense in English; we're treating the two parts ('working' and 'not working') as two single units, so "the [singular entity] doesn't think...". It scans, grammatically. Had the sentence been structured as "the men in the group who work", it would need to be amended to "don't think", because we're treating them as multiple individual units.
Having said that, the syntax is nowhere near acceptable or natural. It's one of those cases where the Danes have excellent understanding of the mechanics of English, but stumble a bit with natural usage.