So I switched off Kaspersky, but there was no change.

Including its email scanner if it has one? It kind of sounds like an anti-virus email scanner is interfering, but since you tried disabling it, I don't know. But, if the email scanner is scanning your messages, you'll want to connect insecurely so it can scan your messages. Then, the email scanner SHOULD connect you to the server securely. Or, if you use TLS in Opera and have an email scanner scan your messages, you might have to accept some certificates from the email scanner so it can man-in-the-middle you to scan your messages. However, I'm not sure how Kaspersky does things. Maybe there are some settings in it for configured email ports etc.

So, you can investigate that if you want before looking for another email provider.