I access my email in two ways from Thunderbird. I have one POP account and one IMAP. The problem is that this makes messages coming to through IMAP marked as read before I actually read them on any account. This is causing a severe problem as I may miss some emails.
The email server is Exchange.
POP is working as designed, here. If you access a mailbox via the Post Office Protocol, you are expected to be transferring it off the server to storage of your own. (RFCs 1081 and 1939 both make this point explicit in their introductions.) From the server's point of view a message that has been RETRieved but not yet DELEted is indeed "read" by the POP client.
If you are using the Post Office Protocol to keep mail on the server indefinitely, then you are in fact abusing the protocol. POP has never required that maildrops hold mail indefinitely. Indeed, RFC 1939 § 8 is clear about the fact that servers are quite free to outright delete messages that you've retrieved but not deleted yourself, let alone simply mark them as read. The Post Office Protocol is, as the name suggests, a protocol where mail is held at a "post office" drop point, from which you collect it and take it away whenever your MUA is connected to the network.
So your question is essentially unanswerable. You are asking how to make POP not work as designed. Of course, this is another case of picking the unsuitable tool for job and then asking how to modify the tool so that it works. If you want a protocol that's designed around the paradigm of having a remote mailbox maintained on a mail server (rather than POP's last-leg-of-the-store-and-forward-chain paradigm) which is accessed by multiple client MUAs, then use IMAP. It's that simple.
