I can't speak as to what is legal in Germany - others may better advise you in that regard - but generally speaking, if you sign the contract, you are legally bound by it.
At this point you should look at the situation with the assumption that they are within their legal right to ask that of you. The question is:
How much will that clause affect you?
Are you the kind of person who works on contracts on the side?
For example, I've worked as a developer for 3 years, and I have never done any contract work - I wanted to focus on my friends/family/hobbies when I got home after 8 hours at my desk. But many of my present and former co-workers did quite a bit of work on the side. One of them went into business for himself. Do you posses that sort of entrepreneurial spirit?
If you are, then this may not be the job for you.
I've read a number of articles recently to the effect that in Germany employers are not allowed to contact employees after work hours, etc. Sounds nice. However, if you read between the lines of that contract clause it sure sounds to me like they're trying to dictate the terms of your personal life. I would be very wary of that.
If you go home after 8 hours of doing good work for them, why does it matter if you chill in front of the TV, or work on a personal project? Most likely these guys don't want an employee getting an idea tangent to their business, going "rogue", and becoming their competition.
You may have no intention of doing that, but are you willing to allow your hands to be tied in the name of their peace of mind?
Also consider the fact that you don't have to tell them everything you do. If you put up/maintain a few websites and get paid a few bucks on the side no one's going to know - personally I wouldn't even tell them. However, you would be doing so at the risk of being terminated if they do find out - again, how much does this matter to you?
Consider anything you sign to be legally binding. If you value your "freedom" as a freelance developer then this job does not sound like the best choice for you. Do you want to ask your boss's permission to take a contract on the side?
On the other hand, if the job pays very well, and/or is a good learning opportunity, then maybe putting aside any personal project for a while is a net benefit after all.