What is the version of your SharePoint?
Whether you want to enable Enterprise Metadata and Keywords feature in a Microsoft list, SharePoint Online list or SharePoint on-premises list?
For Microsoft list, actually, we cannot enable Enterprise Metadata and Keywords feature in a Microsoft list. Due to Enterprise Metadata and Keywords feature needs to work with term sets. Term sets are controlled by managed metadate service, and managed metadate service only works in the SharePoint. So, I suggest you create a list in the SharePoint Online then enable Enterprise Metadata and Keywords feature.
For SharePoint Online list and SharePoint on-premises list, I suggest you check whether managed metadate service is running well and check whether you are Term Store admin.
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