I think one of the most wildest meta/headcanons/theories I've ever come up with so far about Scooby-Doo is that in Mystery Incorporated, the circumstances of Fred's birth must have looked really interesting to everyone outside of Mayor Jones and Brad and Judy.
In "All Fear the Freak", we learn that Mayor Jones was a college student (and, according to Tony Cervone, he was a college instructor for a couple of years, shortly after graduating) when he first came to Crystal Cove, so the earliest age he could be is 18-ish. At some point during this time, he meets the original Mystery Incorporated, and things go from there.
Now, let's remember what has been said about Fred's "mom" in "A Haunting In Crystal Cove". When Scooby sees the picture of Fred's mom, Shaggy and Fred say that she's “Fred's mom”, who "left" when Fred was a baby.
But it was never outright stated that she was ever Mayor Jones's wife, and she "left" and characters act like maybe she'll come back and/or she's worthy of being remembered, as opposed to having already accepted that she's not coming back and being bitter about it. Arguably, there was never a circumstance in the show where they could say she was "Mayor Jones's (ex-)wife" without making it sound weird; usually, if you're talking about your friend's absent mom or dad, you call them that as opposed to their present mom or dad's spouse.
Later in the episode, Fred says that he's into making traps because he wants the people he loves to stay with him and not leave like his mom did. Now, traps are made to catch things before they can flee. While yes, Fred does use traps a few times outside of that purpose (like dragging Daphne into an investigation while she was sleeping), you could interpret this as Fred's mom leaving Fred with Jones because she was afraid of being a parent.
See where I'm going with this?
Mystery Incorporated has fun poking at teen genre tropes, particularly the ones of teens and young adults, uh, going through hormonal stuff and having no idea what they're doing and facing the consequences for that.
So... what I'm saying is that the general public thought that Fred was conceived from pre-marital... relations.
Jones has not been seen hanging around this apparent lady friend for the past nine months. Unless he claimed that it was information he kept to himself (which is possible, since he's been shown to be a private individual, keeping secrets and all), it looks like Fred was born from a brief fling, maybe even a one-night stand.
(Also, I'm gonna say as a note that Jones probably forged Fred's birth certificate and everything and said that the ex dropped the documents off with him. There's also some suspension of disbelief I'll have to ask you to do, since this is still a cartoon and a fictional story.
Additionally, I doubt that Mayor Jones would have forged a marriage certificate and divorce papers, because then he'd have to forge a whole ton of other documents (perhaps even photos, which is probably beyond his ability) and proof that it happened, maybe even create a documents for a fake adult person. It's too time-consuming and he could easily screw up somewhere, allowing someone to catch on. It’d be easier and quicker to say that Fred was, uh, an accident, and that the mother is “gone”, whereabouts unknown. That way, the dead ends will discourage anyone that’s nosy enough to try looking into it, like Fred, who, like any other kid, would inevitably ask “Where’s my mom?”.
Going off of that, she’d probably also fall under the definition of being a deadbeat mom, since there’s no proof (that Mayor Jones had forged) that she pays for child support either.)
It would also contribute to Fred's issues with his "father", because his father never intended to have children as Fred was an accident, and that's why he sucks at parenting and he never quite went through the process of maturing into a better parent either.
I have no idea how this would have affected his reputation for his college instructing and his mayoral campaign - he probably wouldn’t have gotten under scrutiny because it might not have been a big deal, but given that the people of Crystal Cove are shown to be rather apathetic, it's possible that most people didn't really care and voted him in either way.
But, I think it's also part of why the Blakes don't like the Jones (I say part, because there's more obvious reasons that I'll maybe address at some point, but not another time). They don't like Fred, because they think he's stupid. In "All Fear the Freak", when Fred and Daphne announce their engagement, Mrs. Blake blames Mayor Jones for "this". If he had properly parented Fred, none of this would be happening. But... maybe there's also some background to that.
As far as the Blakes see it, history is repeating itself. A young couple is making a rash life-changing decision based on love and emotion. And while their daughter may have some terrible judgment, it's less of her fault and more of her man's fault. Their daughter's lover is a boy who is the RESULT of this kind of love story ending badly — he got his foolishness from his father, and meanwhile, his mother ran off and severed connection with them because she regrets the whole thing.
Even if Jones was already mayor by then (I’m pretty sure you can’t be mayor for that many consecutive years, or it’s at least difficult to do, but maybe I’m wrong and there’s also some cartoon logic on the side.), it’d still look kinda weird that some girl he knocked up a few months ago in some fling dumped their kid on him. So that point still stands.
But I guess in the end, it didn’t really matter that much. Fred finds his real parents, the universe is reset to him having never been kidnapped, and none of this happens. It’s still pretty crazy, though. And maybe I’m just overthinking this.
tl;dr: The public thinks Fred was illegitimate, it was evidence that Fred's parents are terrible parents because one sucks at parenting and the other is a deadbeat, the Blakes think that Fred is dumb because his parents suck and he's gonna repeat history with their youngest daughter, Mayor Jones probably figured “I accidentally had Fred with a girl I liked for a while and she dumped our son on me.” is a better and easier cover story in case someone sticks their nose in places they shouldn’t.
