Isn't accessing private fields and properties due to reflection a security issue?

The question now is, if anyone can access every field in my classes, this is kind of insecure, isn't it?

Not everyone can. Only code with sufficient permissions - trusted code. Untrusted code is restricted quite a bit. On the other hand, if the person who wants to use reflection has your assembly, they can run trusted code on their own machine. That's not a new attack vector though, as if they've got your code they could also modify it to make the field public in the first place.

Basically, if code is running on their machine, you should expect them to be able to do pretty much anything with it. Don't rely on access modifiers to keep anything secret.

So how do I make my Application safe, meaning how do I prevent anyone other than me from changing essential status values inside my classes?

If the hostile user is running your code themselves, you pretty much can't. You can make it harder for them, but that's an arms race which is no fun.

So one option in some cases is not to let anyone else run your code - host it on the web in an environment you've locked down. That's not appropriate in all cases, of course.

If you have to let users run the code themselves, you need to weigh up the downsides of them tampering with the costs of making that tampering difficult. We can't really help you with that balancing act - we don't have any idea what your application is, or what the costs involved are (reputational, financial etc).