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You can make use of this guide when you get sync errors due to duplication rules.

Summary:

Sync errors that happen due to duplication rules in spite of marking the action as Allow instead of Block. Active Salesforce duplicate rules can conflict with Chargebee that inserts records into your Salesforce organization. When Chargebee integration inserts a new record into Salesforce, the Salesforce duplicate rules are run. If a duplicate is found, the record is not inserted into Salesforce. Most of the integrations that work with Salesforce(including Chargebee) which insert records into Salesforce contain their own built-in duplicate matching rules and should be excluded from the Salesforce built-in duplicate matching rules.

Best Practice

The best practice is to allocate a Salesforce license to integration and assign them to a profile specifically set up for the integration user(s). The profile of the user who had connected Chargebee and Salesforce in this case. This profile can then be excluded from firing the duplicate rules.

There are also some integrations(including Chargebee) whose processes(automations) use the user who set the process up as the creator for new records. These should be reviewed as well as they may also cause records not to be inserted into Salesforce. The fix is to make sure the processes are owned by a user that is excluded from the firing of the duplicate rules. 

Example:

In the example below, the matching rules have been configured to run only when the Current User is not equal to our two Chargebee related profiles. This will exclude them from the duplicate checking process.