Can’t they just kindly reply “no” to any foreign governments requests? I’m confused why shutting off all access was the answer when they’re not (to my knowledge) operating in Brazil
What a court in Brazil can do in case of a "no", is then block the whole website, often done in simple ways (DNS) at local ISPs. It can also put the burden on local representatives of Rumble in Brazil, as it did with Facebook in the past (this means jail time for not complying with a court order).
In theory some people below mentioned that it can also forbid local Brazilian entities from performing commerce with the entity (like eg: fining advertisers paying for ads, or the advertise), but I'm not sure how that would work, since I'm not a lawyer.
* Request extradition
* Fine local advertisers
* Confiscate any payments
* Harrass the ISPs who carry the service
* Harrass local users
I do nor advocate any of the above
But the idea a business that trades internationally can say "fuck you" to a nation state is childish
There can be terrible consequences
This often works and rarely lasted more than a day. I don't think I was ever personally affected by one of those blockings when I was in the country.
I don't really remember any case where a large server failed to comply and remained blocked.
EDIT: There are things that were blocked and remained blocked forever, but they're often things like piracy, CSAM sites... which are things that often get blocked even in the USA. Sometimes this is a harsher block directly at the host of the website, either via court order when it's a Brazilian host, or because international laws were broken, or because the host simply complied.
Business implies commerce, monetary transactions. It doesn't imply access however.