Freedom of speech in the constitution
I think this is a very broad question, but I'll attempt an answer. To my knowledge, there is no specific Dutch law that considers freedom of speech on the internet. Instead, there is one article in the Dutch constitution that considers freedom of speech and a prohibition on censorship. That's article 7 of the Dutch constitution (link in Dutch).
It consists of 4 sections. The first deals with freedom of speech in print, the second deals with radio and television, the third deals with (translated by me) revealing thoughts or feelings through means other than the aforementioned and the fourth states that the aforementioned sections don't apply to commercial advertisements.
Since you are asking about freedom of speech online, the third section applies. The section states that no permission is needed to reveal those thoughts or feelings through means other than the aforementioned but it adds two conditions:
In Dutch: "behoudens ieders verantwoordelijkheid volgens de wet". This means that the freedom is subject to one's responsibilities under the law. In other words, other laws may curtail one's freedom under this section. This phrase is also included in the first two sections.
The second condition which is specific to this section is that the law may restrict access to performances (vertoningen in Dutch; not sure if it translates well) to people under the age of 16 to protect good moral (goede zeden in Dutch; again not sure if it translates well).
Restrictions under the law
So the above about constitutional freedom of speech doesn't tell you a lot, it's very general. To answer your question you'd need to know what specific exceptions there are. These exceptions don't need to be specific to statements made online, if it's not allowed in public then the same rule would apply online.
To give these exceptions I'll summarize the information on this page from the Dutch Amnesty International site on freedom of speech in the Netherlands.
Hate speech and calling for criminal acts
The Amnesty article starts with some information on articles of criminal law:
- Article 137 forbids hate against or discrimination of people based on race, religion, gender, sexual preference, or mental handicap.
According to the Amnesty article this covers holocaust denial (considered unlawful discrimination) but not homophobia (when it expresses fear of or aversion to someone's sexual orientation).
Some interesting jurisprudence regarding your question and articles 131 and 132 is this case: ECLI:NL:PHR:2019:1232. It's a Dutch Supreme Court case that considers calls for 'participation in the armed jihad' in the context of the war in Syria. The calls were made in Facebook posts (containing photos of dead victims, photos of ISIS flags, and statements in Dutch supporting jihad). The linked ruling confirms that these posts were in violation of articles 131 and 132 and that the posts were not protected under religious freedom nor as freedom of speech.
Preventing publication of military secrets
According to the Amnesty article censorship (as in ruling some statement against the law before publication) is not something Dutch courts may normally do. It names one exception: when military secrets may be revealed. Then a court may prevent publication, unless the military secrets are such gross violations of human rights that publication would be warranted.
Rights on a platform
I know that European countries have, in some cases, began treating those platforms as public utilities where users are granted rights.
I'm not sure what you're referring to here but I don't think it refers to freedom speech. In any case, after some googling I found a case that is about this: someone filed summary proceedings in the Netherlands because they disagreed with Facebook removing pages on its platform that didn't conform with Facebook's policy on Covid-19. As far as I can see from skimming the court ruling, the ruling holds that freedom of speech does not extend to companies like Facebook having to host your posts. I think it's basically a long ruling that boils down to the well-know XKCD on free speech.
On the other hand, the ruling also points to the service agreement between Facebook and the user. Part of those terms and conditions are entered as facts in the proceedings. Since it's a civil case, I assume users might derive some rights from that if the agreement touches on that.
Another thing that sounds familiar (based on that quote from your question) is net neutrality. Like in the US, that's mostly about network providers having different rules for different content, which isn't allowed in most cases under net neutrality. I don't think there's a freedom of speech angle to that.