The co-founder publicly stated he made the donation on social media. What made him obliged to disclose this? He seems rather proud of it, in fact.

As a result, people feel they may have a moral obligation to not funnel money to him. Your stance also doesn;t really line up with your examples like

Or say your customer base for any reason is in large part Vegan, should you tell your employee's to stop buying meat? Should they stop taking money from the non-vegan customers? How is anyone going to navigate this?

You don't mention the specific problem you have with this, which would be mandated disclosure. By your own words, this is perfectly fine since people can chose the reasons "Anything, including having no reason at all, obviously." to not do business with someone so I'm not sure why it's a slippery slope to you.

No. I'm just of the opinion that I'm in no way obliged to disclose to you what I spend my money on, just because I work somewhere you spend money on.

That's not what you said though. I don't think anyone is arguing that employees of a company are obligated to disclose their spending habits, that would just be ludicrous. However, if that information was available or if the company itself made donations/purchases it's perfectly reasonable as a customer to decide not to support that kind of behavior by continuing to do business with that company.

Just as one example Chick-fil-A is rather famously anti-lgbtq and regularly donates part of their profits to anti-lgbtq organizations. As a consumer it's entirely reasonable and moral to refuse to do business with them in order to reduce the money being funnelled to morally repugnant organizations.