Managing IP blocking while managing self-hosted mail server
Solution 1:
Your definition of "shared hosting" may not be the usual one here. "Shared hosting" typically means that you and many other users share an IPv4 address and you do not have root access to the server. In this case, you do not control port 25 and therefore cannot control the acceptance of inbound email. As it is your hosting provider who controls it, actions to improve the IPv4 reputation would be up to them.
Reading between the lines (please update the question to clarify), it seems you may have a dedicated IPv4 address from a hosting provider, and you are instead using "shared hosting" to distinguish from a dedicated server.
In the case of an IPv4 address which is dedicated to your use and is "dirty", then one of three scenarios will typically apply.
- The IPv4 was added to a few blacklists a long time ago, and has a clean recent history. In this case, the simplest action may be to contact the individual blacklist managers yourself and explain that the IPv4 has been operated by you for X months with no complaints. They typically have a "de-listing form" for this.
- The reputation is trashed, i.e. on many blacklists and/or recently listed to the point where it would be tedious or impractical to clean it up. It is worth asking your hosting provider to allocate a different IPv4 address. Providers have different policies on this. Some will work with you more individually, but if you have a large provider then they may have an automated process where you are assigned a new IPv4 upon request with a limit to how many times you can do so. The provider obviously needs to have spare IPv4 addresses available to the particular node.
- Entire IPv4 ranges from the provider are blacklisted. This can happen due to habitual spam/poor email management policies by the provider. In this case, blacklist providers may not accept de-listing requests. Other than living with the dirty IP, your option here is to change hosting provider.