How does the upgraded ElectrumX server mitigate this issue? Does it keep a blacklist of fraudulent servers and exclude them from the network?
It doesn't... and it can't...
The "bad" servers are running a custom version of the Electrum Server software designed to send the "update required" message and link to malware when they receive a "send transaction" request from a client.
Does the upgraded Electrum client simply block all messages from blacklisted servers? or what is the mechanism for preventing connections to fraudulent servers?
There is no "blacklist"... the mechanism is that the Electrum client no longer just displays the verbatim text that is received back from a server... instead, there is a set list of predefined error messages that it will accept and display... if something "unexpected" is received, the client will display "Unknown Error" and advise you to try again or use a different server etc.
Once I get a message from a fraudulent server, will it get stored in local storage and be likely to be connected to again?
No, the message is received, processed and discarded... There is no action taken to blacklist the server and ignore it.
If I ignore the message, do I simply try to send again, and hopefully connect to a legitimate server?
Yes.
You could potentially implement your own blacklist and prevent outgoing connections to the IP in your own firewall.