If some Vaishnava sampradayas reject the worship of Radharani, how to respond?
Here is the reference to Radharani from the Sri Sampradaya acharya Sri Vedanta Deshika.
nirapekṣa ivaiṣa nīlayā
rasikaḥ pālikayā sa-rādhayā
pṛthag atra kim etad ucyate
kuhakaḥ kaścid asau kulasya naḥ
Commentary by Sri Appayya Dikshit: nirapekṣa iti arasika nīrasa-hṛdaya eṣa kṛṣṇa. nīlayā sa-rādhayā rādhayā sahitayā pālikayā ca nirapekṣa iva apekṣyata ity apekṣa. karmaṇy apratyaya… apekṣaṇīya-kṛtya-rahita evety arthaḥ. Ivakāro ’vadhāraṇe. nīlādayo gopikāviśeṣāḥ. atra gopikāsu pṛthak nīlādikā pratyekaṁ udāhṛtya. kim etad ucyate? asau kṛṣṇa? na asmākaṁ kulasyaiva kaścit kuhako vañcakaḥ.
Translation (according to the commentary): Krishna, devoid of any rasa, behaves in an unexpectedly dejected manner with Nila, Palika and Radha. They then ask the other gopis, “Is this our Krishna?” and they reply, “No. He doesn’t seem to be from our group. He seems to be a cheater.” (Canto 9, verse 90.)
Bibliography — Translated by Hari Parshad Das from the Yādavābhyudaya with the commentary of Appayya Dikshita, Volume III. Sri Vani Vilas Press, Sri Rangam. 1924.
(I thank my friend and scholar Hari Parshad P for providing me with this reference)