Once I thought that my IP is blacklisted, because sereral MX tools told me so.
But I was/am not. I have two internet connections. One is DSL (dial-up) with alternating IP adersses and one ist DSL (dial-up) with fixed IP address. Dial-up connections like DSL and others where IP adresses change are generally not defined as MX IP adresses. It depends from the definition of the IP Range that your provider publishes. If your provider does not mark your IP address (range) with a kind of MX flag, your ip address will be blacklistet by MX tools and mailsservers do not accept mails from your IP.
Maybe it helps finding the reason for your “blacklisting”.