The cancer label warnings in California aren't violating any free speech, this is the same thing so it wouldn't violate it. All the browsers would say is "The European Union has verified the identity of this site owner" or something similar.
>"The cancer label warnings in California aren't violating any free speech"
That's because it's commercial speech [0] attached to a sale of a product, which gets a reduced level of protection. I'm don't think that you could, in the US, compel non-commercial software to express messages like "We trust this CA". Mozilla has a 1st amendment right to not trust to CA's, and to tell their users why they don't trust the CA; to boycott a CA; to implement this in code and ship it.
> Mozilla has a 1st amendment right to not trust to CA's, and to tell their users why they don't trust the CA; to boycott a CA; to implement this in code and ship it.
Nothing so far says that Mozilla can't tell its users that EU trusts this but Mozilla doesn't. However it is clear that it is intended to force Mozilla to at least gives the user the choice to trust EU on this.
The part where they're forced to provide the EU's alternative version is still compelled speech.
The decision of trusting or not trusting a CA has an expressive character; it's not pure machine math. Some of the decisions are political speech, even: "we don't like the policies of country X, therefore we'll boycott their root certificate". (Roughly characterized)
I feel there is a big difference between a mandated warning label (California cancer labels), Vs a mandated endorsement like forcing browses to say that unsecure connection is secure.
Sure there is a big difference, but not from the perspective of free speech. Both cases forces you to display a label even if you don't want to show it to people. It is understood that the label isn't your speech, hence it doesn't limit your free speech rights.
You might object to this for other reasons, but free speech isn't a good reason.
https://en.wikipedia.org/wiki/Compelled_speech
Whether or not it would violate the 1st amendment would be up to the courts to decide.