Depends how you use it. When someone uses a font like Comic Sans sparingly, you can infer there's something special about this text. That maybe, this particular snippet is either a joke, or an informal formulation, or an XKCD quote. It can indeed be the author signalling that this snippet should not be taken very seriously.

But if the font is used by default, you cannot reasonably infer credibility from it. If the whole thing feels less credible or less serious anyway, then it's a status issue.

It's like someone showing up to give a talk with a Hitler hairstyle and toothbrush moustache. There's nothing wrong with the hair or the moustache per se, and perhaps they are your favourite for some reason, but the pre-associations will be distracting to people.

And now I'll Godwin myself out.

Serif fonts aren't more credible than San serif fonts. Serif fonts are great for lots of paragraph based text, san serif fonts are better for titles and shorter passages...and also code.

Fun fonts can be serif or sans, and are generally more artistic and ad oriented.

On screens you are right.

But on paper, with much higher resolution, serif looks more serious.

Sans often appears on signage, especially in Europe, where it works very well.