With Gmail, sent messages are part of the conversation. So, with Gmail IMAP, you have a copy of the sent message from "[Gmail]/All Mail" and a copy of the sent message from "[Gmail]/Sent Mail". Since "Sent Mail" is set as the IMAP sent folder in the account's properties, Opera will treat the copy from "Sent Mail" as a sent message that can be controlled by the "show sent" option for each message list. However, for the other copy that's from "All Mail", as far as Opera is concerned, it's just a received message like any other received message and there for isn't controlled by "Show sent".
To work around this, you can create a label in Opera to match a from header that contains your email address and set the label to "hide these messages from other view". Then, you'll be able to uncheck "show hidden" for each of the views you want to hide the sent copies from "All Mail".
Note that with Gmail IMAP, it's best to not user any of Opera's views in the mail panel except for the "you@gmail.com" access point. Drag that access point so that it's at the top of the mail panel and collapse/hide/ignore everything else. Then, use the Inbox IMAP folder view and other IIMAP folders that represent Gmail labels.