Preface: Photographic light meters are practical instruments designed for use by photographers, they are not scientific instruments designed to CIE standards. The ISO Guide (not a standard) 2720:1974 does not define what the angular response of an incident meter must be - it is left to the manufacturer to decide. "Any form which allows satisfactory determination of exposure..." ISO 2720 does give guidelines on the angular response of cosine and cardioid receptors, if they are the chosen forms. The most important thing is to calibrate your photographic system as a system, and then to use consistent technique with adjustments based on experience.
The 'correct' spherical response of a flat receptor is cosine: ie there should be no response at all to light from the side and full response to light from the normal. The shape of the response is like half a figure-of-eight: a sphere sitting on the receptor surface. (The response of a dome is usually described as cardioid - ie it should have a limited backwards response to about 145°, which is often blocked by the meter body.)
When I got my L-508 I wondered about the difference between a flat receptor and a retracted dome (it seemed too easy when compared to swapping receptors), and compared the readings with my Studio Master with a flat receptor, my Spectra meters with flat receptors fitted, and a grey card (which behaves like a flat receptor, not a domed one). The agreement was close enough in terms of angular response, once the systematic differences had been allowed for. If you are really interested I could do a more detailed analysis of the retracted dome against the ISO values for a cosine response.
In practice many domed meters are used with a cupped hand when assessing the contribution of different lights - this is analogous to a retracted dome.
There is a small difference in effective calibration between the dome and retracted dome for the Sekonic meter. I don't know about the Starlite (sic). With the dome out, the incident reading is equivalent to the same meter doing a spot reading from a 12.5% (approx) grey card - though the angular response ('indicatrix') of a grey card is different from that of a dome. With the dome retracted the incident reading is equivalent to a spot reading off a 14% (approx) card. Little difference in practice.
So, it's something to be aware of, but in practice it is unlikely to make any difference. I'm happy to use the retracted dome of my L-508C for repro and for for assessing the contributions of different sources.
Best,
Helen