Problem identified

The table #__fields_values is not normalized.
In simple words we have repetition of information (value) between this table's rows and the #__fields table.

The inserted values seem to be stored as a json string in the fieldparams column of the #__fields table

{"multiple":"","options":{"__field10":{"name":"Computer Science","value":"Computer-Science"},"__field11":{"name":"History","value":"History"},"__field12":{"name":"Poltics","value":"Poltics"}}}

This is jeopardising the referential integrity of the data, as the only responsible for that, is the code used for saving them.
E.g. If we made a change in a value, this change has to be reflected in all the tables, where that value is present.

Proposed solution

Create 1 more table for the values, where each value will be saved and will have a primary key.
Then use the PK as a foreign key to the table _#_fields_values (or wherever they are used).

Open questions

This requires changes in the code level beyond the schema changes. Is this a long shot atm?
Not sure if it will cause any B/C issue or any other issue (e.g. with the plugins).
I can prepare a PR for that, in case you agree in principle.