There is hereby a failure of human language usage: The word “consensus” is overloaded.
In Bitcoin, the word “consensus” has the very specific technical meaning. It does not refer to an agreement amongst humans, as in colloquial usage. Rather, it denotes the resolution of a synchronized state in a distributed system.[...]
In Bitcoin, the consensus means that all nodes arrive at the exact same conclusions about the current global state of the blockchain ledger: The set of valid transactions that exist, the meaning of each of those transactions, and the order of those transactions.
You are of course right, the usage of the word in this thread is a bit ambiguous/imprecise, but I think neverless the discussion here has to do with consensus.
The "global state" of the blockchain can be altered only following the strict rules of the Bitcoin protocol. Even if I don't double spend a coin and follow other basic rules of the Nakamoto consensus, I cannot simply come up with a new transaction format or use another hashing algorithm. I have to respect these rules and formats, and only then my messages (i.e. transactions) will be taken into account by the algorithm, and resolved according to the Nakamoto consensus.
Thus, hard and soft forks change not necessarily the general principle of the Nakamoto consensus, but other rules that are part of the Bitcoin protocol, which determinate the global state of the blockchain. Hard forks could
in theory even change the general Nakamoto consensus principle, e.g. like Ethereum planned the transistion to Proof-of-stake. (Not that I think that would ever happen in Bitcoin.)
But maybe here we shouldn't talk about "the consensus" but about "protocol rules" or "consensus rules", or "how consensus rules are established".