I agree with RobM.
So it would be possible that they share everything they know about me with (american) governmental organizations.
Yes, very possible.
Are there even alternative browsers which wouldn't do this?
The Onion Router. There may be others. Even Firefox will work this way if you use local syncing, and disable malware and phishing protection. Personally, I would not disable those.
Can you trust Firefox?
I don't think this is a Firefox issue. This is a government issue. For example, you can read about telecommunications data retention in various countries. The Electronic Frontier Foundation has a good write-up about the Stored Communications Act.
You should note that
synchronization usually means your data is stored online. I am aware that local syncing is possible. However, because of the wording, they are likely storing your data online ("in the cloud"), and are required to hand it over to the proper authorities if compelled.
Let me reiterate: If, as a company, you're storing information online about users/customers, then in many cases you can be required to hand it over when compelled by law enforcement. If you are not storing information, you don't have to hand over what you don't have.
Firefox is storing information if you allow it. This is a very convenient feature which has the added affect of being held to government data regulations. If you ask me, Firefox is very trustworthy. However, do you trust the government of your country?
Even simple Metadata can be used to quickly identify you
Because of Metadata, whether this is encrypted or not may be irrelevant. They may be able to decrypt your cloud-stored data. Even then, it may not matter due to certain laws in certain countries. Wait, what?
For example: user connected to
X server at
Y time may be all they really need. As an example, you could be in China and end up visiting a website associated with Falun Gong. For Firefox to operate in China, they would be compelled to cooperate with Chinese law.
They may store your meta data details, such as the IP address you connected to before checking if it was a malicious website or not, even if you're behind a VPN at the time, your previous profile was associated with other IP addresses.
This is just a rough example of how meta data can work, and is not necessarily relevant to you. It's my hope that this would explain how powerful meta data is so you can apply it to other situations.
Firefox's Built-In Phishing / Malware Protection
Let's see what Mozilla has to say. How does built-in Phishing and Malware Protection work?:
"Firefox will request a double-check to ensure that the reported site has not been removed from the list since your last update. This request does not include the address of the visited site, it only contains partial information derived from the address."
This partial information / metadata = exposed as a rebel sympathizer. The Death Star is on it's way.
If you don't like that idea, then don't sync online, and don't use the built-in phishing and malware protection. Personally, I don't like the concept of syncing in many situations. However, I will use the built-in phishing and malware protection as it helps minimize the amount of work I have to do while surfing the web, and it protects me!
Mozilla is up-front about what they are doing. They are not lying to you.
So why does Firefox cooperate with the government?
They have to. And why wouldn't they? In many cases, there are very good reasons to do so, for example, to track down criminals. Obeying the law is a cornerstone requirement to doing business in any country. If you don't like a country's laws, you have the choice to leave, and not do business there. Try to break those laws, and see how long you last.
Unfortunately, there are also cases where countries do not offer fair trials, and would quickly imprison, or even execute anyone caught engaging in banned activities, such as religious organizations like the Falun Gong. Again, if a company doesn't like the laws of a country, they may leave.
Raising awareness and fighting against corruption is one thing, and beyond the scope of this answer, but you can't expect to do any kind of business in any country, unless you obey their laws. And that's why Firefox provides this disclaimer. They are telling you the truth, even though they can hide it from you.
If you ask me, Firefox is very trustworthy. I don't know what your government is up to, or if Firefox has a presence in your country, though.