I have created a group which doesn't have replicate permission, but when I click on the page sidekick "Activate Page" I am receiving message: "Warn: No rights to replicate, Request for De/Activation issued for <website page path>", also it is triggering a workflow for activation.
Why it is happening and how it can be resolved? Please let me know. It is related to classic UI mainly.
This is actually an expected behavior, if not to say: a feature.
If you try to publish a page but don't have the according replication permissions, AEM will start a "Request for Replication" workflow for you. OOTB that request will be assigned to admin but this can be customized based on your requirements. There is blog article  outlining the according mechanism (it's a bit outdated, but the general approach is still valid).
Please also note that there is a corresponding mechanism when unpublishing or deleting a page ("Request for deactivation" workflow) and that deletions automatically trigger a de-publication.A common case where these workflows apply unintentionally is if references should be replicated (e. g. assets) but replication rights are missing for the referenced content.
If you attempt to change the OOTB behavior, please plan for the underlying use case: what should happen if a user tries to replicate (also indirectly through references) content without according permissions?