It is possible to use Cloud Native Synchronizer and Self-Hosted synchronizer at the same time, but it is extremely important not to use both of them at the same time to synchronize the same projects.
This is caused by the the fact that Cloud Native and Self Hosted are two separate versions and there is no communication between them. If you synchronized the same projects with both synchronizers, every self-hosted synchronizer update would be interpreted by Cloud Native one as a user-made change and synchronized again. This, again, would be interpreted by Self-Hosted as another change and, as an effect, you would deal with a synchronization loop.
There are no obstacles, though, to use both synchronizers for different, unrelated projects.
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