This doesn't make sense to me.
What it is saying is that, to get around a hard fork (and a soft fork), some miners will mine a new block type.
This new block is at 1MB, but can "expand" to bigger than 1MB, by allowing included txs to fall outside of that 1MB limit
and into the "mushroom" section of this new block. When you are in this section, you can not see, verify, or spend (technically).
That means when people use bitcoin, they won't know if their tx will be within the 1MB or the mushroom section.
This alone will cause too much damage to the market place, especially with merchants.
Bitcoin is based on a provable tx. Your now saying we won't be able to prove or see some txs.
It would require that all miners have upgraded, and they all produce a new type of block that can contain more than 1MB of transactions.
People with updated software will be able to view/spend transactions in the new type of block, but people with the old software will find that some of their transactions fail.
Any damage this proposal would do, a hard fork would do too, but probably worse.
A hard fork could result in a merchant caught on the wrong side of the fork sending out an item they think the've received a payment for, when the transaction never existed on the winning newer fork.
In this mushroom blocks scenario, the merchant would just think they had never received the payment if it ended up in the mushroom block, but as soon as the software was upgraded, they would then be able to see that a payment had been received and dispatch the item - without the risk of losing Bitcoin.
Everyone would pretty quickly upgrade you would imagine once they were not receiving payments, and the people sending them told them they need to upgrade.