How will it harm Dutch culture?
The same way any culture is harmed, when it allows those holding views in opposition to said culture to grow in influence.
I think they can keep their culture how they like it. They just can't force others to participate.
Nobody is forcing others to participate; they are just banning others from engaging in practices that are in opposition to Dutch Culture.
And there is nothing wrong with that; if you don't like Dutch culture, you can always move back to where you immigrated from.
Indeed, I have to wonder; why immigrate, if you intend to abide by the culture of the nation you immigrated from, and not the nation you immigrated to?
If a natural born citizen
That term doesn't apply to the Netherlands; it's something particular to the US.
It can't even be used in relation to the Netherlands, as being born in the Netherlands is insufficient for citizenship.
If the Dutch don't want women wearing burqas, then tell them why. Persuade them. The government isn't the fashion police. Somehow I think Dutch culture is strong enough to overcome bad fashion.
Or, compell them. What you are asking is for the Dutch to accommodate the practices of other culture in the Netherlands despite those practices being in opposition to Dutch culture.
Why should the Dutch have to do that? Why should their democratic will be ignored?