My rent is due on the first of the month and there is a large late fee if the rent is received later than the first. I send my rent check in before the first but date the check for the first of the month. Can the landlord cash the check before the first of the month? Is it legal to post date checks in WA? Since the rent is not due until the first, if they deposit the check prior to the first, would they technically owe me interest?

A post dated check is not illegal in WA. However, a check is defined as a draft drawn on a bank that is payable on demand. A post dated check doesn't meet that definition. If the requirement is to pay your rent by check, then they could deposit it. And no they would not owe you interest or penalties for cashing it early.

In fact it is generally held reasonable to mail a payment several business days before its due.

What I would do is see if the landlord would accept electronic bill payments or use a bill payment service to send them a check to show when the payment was sent.