Correct. Like Ripple, Stellar requires special (and dangerous) trust in certain nodes.

This is incorrect. A trustline between a user and a gateway is no different (https://ripple.com/wiki/Ripple_for_Gateways#Gateway.E2.80.99...), special or any more dangerous than a trustline between any two users on the network.

I can extend a trustline of $20 to my buddy Jim or I can extend a trustline to a gateway for $20. It makes no difference to the network.

For example, gateways (https://www.stellar.org/blog/introducing-stellar/#gateways) have to be trusted by the Stellar network as they send messages like "a user deposited 100 USD via a bank wire transfer, so please accept this digital representation of 100 USD, trust me".

Also incorrect. The only trust required is for the user to trust a gateway to hold a balance on their behalf. The consensus process--you might want to read about it at https://ripple.com/wiki/Consensus ensures that the all nodes agree to this change in the status of the ledger.

This trust is dangerous as people running an (initially) honest gateway may start acting maliciously and lie about how much USD or EUR or other currency exist on the network.

Wrong again. Both Ripple and Stellar's consensus process require that all of the nodes agree on the state of the ledger before any new transactions can be added to it. Bogus transactions or changes to the ledger are easily detected.

From Ripple's wiki (https://ripple.com/wiki/Consensus#Liars):

If someone should be dishonest, the honest actors will notice them lying and can disregard their future attestations. That is, if you lie once, you have no gain as the network doesn't care and they won't care what you say in the future.

The ripple protocol requires validators to sign the consensus ledger after each validation interval. If a validator fails to do this, it will be easily detectable. Similarly, if a validator signs a ledger and then signs a ledger after that which cannot be reached by a combination of valid transactions, this will also be easily detectable.

And then you say…

By the time the malice is detected, maybe the network could trace all USD or EUR that was issued by the gateway, and revoke it, suddenly pissing off a lot of users who owns this currency as it would disappear from their wallet. Users would then loose trust in Stellar, and the network would collapse...

Nope; see above why this can't happen.

Stripe would presumably be the first gateway trusted by the Stellar network. Okay, so what if Stripe decided they could not trust other gateways and wanted to remain the only gateway?

The model isn't based on trusting any particular gateway; it's based on trusting multiple gateways to not collude against you.

Example: you may not trust a gateway run by the Democratic National Committee or one run by the Republican National Committee, but you can be pretty confident they aren't going to collude against you. And because they'd both are on your Unique Node List, if they agree with the other nodes you talk to, you can be confident the ledger reflects the true state of the network.

Well Stripe would be the only way to inject USD or EUR or other currencies in the network, effectively making Stellar a fully centralized digital currency, with the entire Stellar network being dependent on Stripe not being hacked, not being abused by a malicious employee, not shutting down, etc.

Wrong. Again.

Anyone on Ripple (or Stellar) can be a gateway or market maker and provide liquidity on the network. There's nothing special about Stripe, except that they have more money and reputation than most of us do.

It does mean that lots of people will trust Stripe to hold USD balances on their behalf.

If you're totally paranoid, with Ripple or Stellar, you can decide to only transact fiat currencies with people you know and trust and act as gateways for each other (https://ripple.com/wiki/Ripple_for_Gateways). The beauty is you can transact with people outside of your circle if one of your friends has extends trust to someone you don't know. You don't have to trust them, but as long you trust someone in common, you can transact with fiat.

This is the complete opposite design principle of Bitcoin which requires absolutely no trust in any specific authority.

Because the bitcoin protocol doesn't take into account the concept of gateways between the blockchain and fiat currencies, bitcoin users are left with relying on exchanges like Mt. Gox to address this. How did that work out?