Weak, and with money.

Sure but on the other hand it's nice to have money in order not to starve.

If you're running a business, whether you need professionalism really depends on what you're doing.

Medical software? Anything aimed at governments as your customers? Billing? Be professional.

Literally a thing aimed at software engineers? Book publisher? Most types of online stores? You can be quirky

There is a place and time for both.

If my bank used it I would assume
1: They are compromised
2: They are cringe

Well. Companies, people about to pay for those companies for professional stuff...

I personally expect professionalism from government websites. And when buying products and services from private companies, a professional looking (and well working) website is something I want to see. Makes it more credible for me.

If the technical parts company I'm contacting has a poorly functioning website with anime shit in it, I'm definitely not going to run that by my boss lol. Sometimes the cartoon things can be used to distinguish yourself from the competition of course but I wouldn't gamble on that in my field.

There's a time and place for everything.

Tbf, it can be a harder sell. For instance I'm recommending Delta Chat to my contacts over Arcane Chat even though Arcane has some extra features like Markdown support, because Arcane has a weird Chibi wizard girl mascot when you first open the app.

I don't need them assuming I'm into hentai or some shit just because of my choice of messenger, or just getting the ick and so they keep using FB messenger. Also, in fact I like anime but I've also always hated the Chibi artstyle, I like like, Trigun and Mazinger Z and stuff. Even then, anime is stereotypically too horny for me to want to associate with it without being able to explain how "yes most of them are, that's why I'm extremely picky and choose mostly space violence, but there is one good horny anime called Golden Boy." Also there's a difference between those who like anime and those who's entire personality is liking anime, the more web based things that have anime branding that I try to convince friends to use, the more I look like my whole personality is anime when in reality my whole personality is Privacy (and Piracy and kitties and hobbies and... but ykwim), and all that is before we throw in the furries, while they constantly insist it isn't sexual, nobody is believing that shit (I'm sure it isn't for some but c'mon there's too much furry porn out there, we know already, it's clearly sexual for a large contingent of people drawing furry futa.)

Tl;dr I get why some people wouldn't want overly sexualized or possibly divisive (in a sense, not like politically but that isn't the only context that word can be used in) cartoonery in logos and mascots, especially when it isn't also their thing or they don't want their mom asking weird questions about a meaningless logo.

I agree

It doesn't carry the sort of seriousness and relation to the business/work that many associate with professionalism.

having the qualities that you connect with trained and skilled people, such as effectiveness, skill, organization, and seriousness of manner

It's of course subjective but in most situations, I don't think catgirl anime stuff really fits.

Yes, but paying to support open source software is a decent compromise.