I'm in the Netherlands too. I also have a (Dutch) law degree. That does not make me an authority, yet if your product and theirs are not in the same industry or in another way in competition, I can't think of any legal grounds on which this clause can be enforced, but several of why it can't be. That said there is a real chance that pressing the issue is going to make the relationship turn sour. Remember that in your first month you can be fired without cause, without compensation. You likely also have an employment contract of limited duration (1 year?) which they don't have to prolong.

An alternative is to not give up your company and hope they fire you, and then sue for unfounded dismissal. This can be quite lucrative. I wouldn't want to wage a legal battle in a country I just arrived in, in a language I don't speak though.

If you speak Dutch there is a quite good forum that often has useful advise (in addition to consulting a lawyer, not instead of).

The union advise below is, as much as I dislike them, good - for little money they will help you out with this. A legal assistance insurance isn't going to cover this issue at this point, if you didn't have one before this whole thing started.

Also I'm really curious on what company this is, and what country you're from.