A few differentiated issues here:
1. Roland Koch, erstwhile Premier of Hesse, committed to a total night flight ban in exchange for getting an OK from mediation conference to build the 4th runway, then went back on his word. Not surprising hat folks got pi$$ed off and took legal action.
2. The 4th runway puts traffic over areas that have never experienced significant aircraft noise in the past. Not surprising that they're tad peeved.
3. Lufthansa Cargo has few options, given that 50% of its traffic is flown on a combination of freighter and pax flights. Anyone who says that they should move the freighter fleet to different airport misses the point - express traffic (which is a significant proportion of total traffic and over-proportionately profitable) won't tolerate any delay.
4. Lufthansa Cargo has done SUCH a crap job of selling the need for night ops. Instead of moaning about €40m annual losses and job cuts, they should have been banging on about the impact of a night ops ban on the ability of German manufacturers to compete in the world market/stressing the knock-on effects of the volcanic ash on production lines/ painting a lurid picture of convoys of trucks blasting through the countryside from Hahn to FRA, polluting the atmosphere and creating monster traffic jams etc.
5. The media has done a excellent job for the protesters, publishing foreshortened telephoto images of an A380 appearing to miss the spire of Mainz's cathedral by millimeters and interviewing logistics "experts" who "haven't actually studied the express logistics concept".