Yes, and this popular opinion is one of the exchanges and online wallets. Not necessarily the miners or nodes running the network.
Yes, popular opinion can cancel you via forking the blockchain or software.
which kind of goes against the very philosophy of bitcoins in the first place, where there should not be centralized control of the currency. A blacklist of coins is a defacto centralized control.
On the other hand, the lack of centralized control means that each person can have their own philosophy of bitcoins. Literally every individual can have their own belief about what bitcoins are useful for. The only limitation is whether a particular philosophy makes sense in light of how bitcoins work and behave at any given moment.
To use the recent parlance, can my money be "cancelled" by popular opinion?