Seems to me this is a problem with the tools you are using, those are not entering the SRID correctly. I can easily insert geometries with a spatial index on the table and a SRID.
To see what has been executed, check v$sql:
select sql_fulltext, parsing_schema_name, module f rom v$sql where parsing_schema_name='your_schema_name' and module is not null;
If you know what your application's name is inside Oracle you could change module is not null to module='your_module_name';
Well Stefan's comment is in the right area. I think there is a conflict between you, the database and/or your application. For instance your metadata is incorrect for 3857 which is Spherical Mercator, not geodetic. So I don't think it will solve your issues but alter the metadata to something like
INSERT INTO user_sdo_geom_metadata(
) VALUES (
SDO_DIM_ELEMENT('X', -20037508.34, 20037508.34,0.05)
,SDO_DIM_ELEMENT('Y', -20037508.34, 20037508.34,0.05)
In general the element mins and maxs are ignored by all parties. But its possible your application is sniffing the 180s/90s and deciding you really have geodetic information. Not sure.
It would be interesting to know what SRID the application is inserting. Seems to me you can just drop your spatial index and let the application do its thing inserting some records. Then look in the table at the SRID that was inserted and report back to us.