The solution was changing the Transfer Record Permissions in Profiles -> Pick your profile -> system permissions -> Transfer Record set to true.

FYI for others following this issue: Kyle got this resolved by adding the Transfer Record permission to the appropriate users’ Profiles/Permission Sets.

The cause of this issue was this: In Banzai Update 7, we made some changes to properly enforce the “Transfer Record” Salesforce security permission. Here’s how this permission works: if you’re currently the Owner of a record (or a member of a Queue that owns a record), you can transfer the record (that is, change its Owner) to whoever you want. You own the record, you have this right! But if you are not currently the Owner of a record, you can’t change that record’s Owner unless you have the Transfer Record permission (and/or the Transfer Case permission if you’re dealing with Cases, or Transfer Lead if you’re dealing with Leads). This is a security restriction that is enforced in the native Salesforce UI, but Skuid has not enforced this properly up until the recent release.

So if anyone else is having this issue — if your users are suddenly unable to change the owner of records that they are not the owners of, you will need to consider adding the Transfer Record permission to these users’ Profiles/Permission Sets, otherwise the operation(s) they are performing would violate the Salesforce security model.