They'll likely discover that GDPR is not that optional as soon as a customer (or a competitor with a grudge!) reports them to their relevant national privacy/personal data protection authority, after which they'll get to have a very uncomfortable conversation where they will not be able to use those arguments
(Do you regularly check to make sure you're obeying laws in countries you don't ever intend to visit? No? Then why should Kagi?)
I suppose a serious breach of regulations, and if Kagi decided to ignore fines, apart from a bad reputation, could ultimately lead to things like judicial decisions of blocking access to the website or blocking payments for EU customers.
The scope of GDPR is clearly including businesses operating from the US, but has any company registered only in the US ever been fined by EU?
This means they're exposed to GDPR not only indirectly by serving EU citizens but also directly by operating within the EU.
Honestly I get the T-shirt part this way. You got to Doo crazy stuff as a start-up. I also get that you try ai stuff. As long as you keep up de search.
However what scares me is the apparent lack of knowledge about privacy, gdpr and what is PII in a product that, to me, is all about privacy. Have one person in the company be an expert in privacy and GDPR etc and use their insights, since it is critical for your right of existence.