If by "our constitution" you mean the U.S. Constitution then no, it says nothing of the sort. The first article of the U.S. Constitution concerns the organization of the legislative branch. You may be referencing the Equal Protection and Due Process clauses, in the Fifth and Fourteenth amendments, but neither of those applies in this situation either since there are no laws or governmental actions at issue here, and random sites on the internet are not universally considered to be public accommodations. Even in the ADA context, the law isn't actually clear, since websites aren't specified anywhere in the text at the federal level and there's no SCOTUS precedent on point.
Some states are more stringent with their own disability regulations or state constitutions, but no state anywhere in the U.S. has a law that says every visitor to a website has to be treated equally.
You can assume it's the USA and that I'm just dead wrong, but the third word of my profile specifies where I'm from and you'd find that this Dutch constitution matches the comment's contents
Equal protection is indeed not the same as equal treatment. No, it really does say that everyone shall be treated equally so long as the circumstances are equal (gelijke behandeling in gelijke gevallen)
I didn't assume, that's why I started my comment with "if by what you mean." Good to know that you were referencing a different place, but it's unrealistic to expect people to delve into your account bio to understand what you intended by "our constitution," especially when the parent comment also contained no geographic or cultural references. Perhaps you know the parent commenter and know that they share your geography? If so, that would also have been helpful context.
As an aside, I'm curious by how that language in the Dutch constitution actually works in practice. Is it just a game of distinguishing between situations or people to excuse disparate conduct? It seems like it would be unworkable if interpreted literally.