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But soft forks are hard forks and hard forks are soft forks For example, how hard was BCH fork on BTC? How hard was Taproot and SegWit on Bitcoin?
We have definitions what counts as a soft fork vs hard fork. BCH was a hard fork since they are no longer part of our chain. Taproot and SegWit were soft forks since old nodes can still sync to the same chain as new nodes.
A hardfork is a change to the bitcoin protocol that makes previously invalid blocks/transactions valid, and therefore requires all users to upgrade.
Any alteration to bitcoin which changes the block structure (including block hash), difficulty rules, or increases the set of valid transactions is a hardfork. However, some of these changes can be implemented by having the new transaction appear to older clients as a pay-to-anybody transaction (of a special form), and getting the miners to agree to reject blocks including the pay-to-anybody transaction unless the transaction validates under the new rules. This is known as a softfork.
Therefore, I would say hard forks are not forward compatible (old nodes don't see the new chain as valid) while soft forks are (old nodes see the chain as valid - even though they might not fully understand what's going on there).
trying to take away some of the stigma of a hard fork
What kind of stigma? That bitcoin hard forks are taboo?