Indeed Pieter was the first 'commoner' to marry into the royal family and he didn't get a title upon marriage (as i understand it because then Q.Juliana was not a fan of titles). To some him being a commoner was already a bit of a shock and in certain circles he was looked down upon a bit in the early years.
Pieter proved himself a very approachable person, very outgoing and easy to talk to. He also has a good sense of humor, also about himself and his own role. Where the dutch royals could at times be pretty stand-off-ish, Pieter has always been very jovial when interacting with the general audience and also journalists. Sometimes so jovial that sometimes it bordered on a little bit 'silly' (it's not the right word, but i can't think of the right one in english).
Also Pieter performed piano concerts with a few well known pianist friends, also on a few tv shows, which made him probably feel even more down to earth to many of the general audience (maybe not so much in the royal family, i think Q.Beatrix was necessarily a fan of this)
In the NL it's quite common to make jokes about or parody celebrities, politicians etc, and we like when the celebs can laugh about that themselves; Pieter with his very recognizable look, with the glasses and the large ears was always easy parodied, and he was not one who minded it at all.
The clips shown a few posts earlier are by very famous dutch comedians, and although at the time it was a tiny bit daring to joke about someone from the royal family, looking back the humor was pretty gentle and without intending harm. Maybe it was even a bit of an honor to be parodied by them, and as said, Pieter was always known to have a good sense of humor.
Over time and also due to several patronages Pieter has done, appreciation for him improved, both to the general audience, but also within the royal family.
maybe an interesting read is this article (in dutch, but i hope you can use an online translator for it)
Profiel Pieter van Vollenhoven: doorzetter met grapjes