Its gonna depend on specifics in the law. Is it about
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a software component that allows viewing a web page.
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software that is marketed as an internet browser
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software that is being used to connect to the web
Many software is or can technically be used to browse the web. Thunderbird as a notable example is a mail client but is a capable of displaying any weburl. Some of the software i use on my job is capable of doing the same. Visual studio can do this. It used to be a very common feature.
The ad window when you start steam works like this and the inbuild steam Browser aside the entire steam store also functions as a locked down browser. It even shows a url bar but at least here you cant enter any url.
Depending on the law these softwares need to either comply or be excempt.
With self hosting getting popular and the trend of webapps (many of the self hosted ai apps) you dont need to be online to have a valid usecase.
If i go on holiday to France, never connect to any french internet but use a self developed browser to acces a local run webbapp am I suddenly a criminal?
If i am an open source developer workin on any of the plenty of github repos that rely or build on mozzilas open source code am i a criminal? Should GitHub be blocked because it provided acces to those repos to the french?
I do agree if mozilla has a registered company in french that those could indeed be targeted by the government but if there not surely they cant
be blamed by simply ignoring foreign laws.
Piracy and porn can have wildly different laws around the world i only ever heard of countries blocking providing domains trough isps and never that far away foreign companies are supposed to take notice of local Law.
The account thing matters because this establishes a relation of client and service provider. Facebook services millions of european customers and businesses of which it actively manages data.
Mozilla in contrast mostly just build a tool that any anonymous internet person can use for themselves.