māṁ hi pārtha vyapāśritya ye 'pi syuḥ pāpa-yonayaḥ striyo vaiśyās tathā śūdrās te 'pi yānti parāṁ gatiṁ

mam hi partha vyapasritya
ye 'pi syuh papa-yonayah
striyo vaisyas tatha sudras
te 'pi yanti param gatim
"O son of Prtha, those who take shelter in Me, though they be of lower birth-women, vaisyas [merchants], as well as sudras [workers]-can approach the supreme destination."
If one actually wants to serve Krsna, it doesn't matter whether one is a sudra, vaisya, or even a woman. If one is sincerely eager to chant the Hare Krsna mantra or diksa-mantra, he is qualified to be initiated according to the pancaratrika process. According to Vedic principles, only a brahmana who is fully engaged in his occupational duties can be initiated. Sudras and women are not admitted to a vaidika initiation. Unless one is fit according to the estimation of the spiritual master, one cannot accept a mantra from the pancaratrika-vidhi or the vaidika-vidhi. When one is fit to accept the mantra, he is initiated by the pancaratrika-vidhi or the vaidika-vidhi. In any case, the result is the same.
Regarding mantra-siddhi-adi-sodhana, the efficiency of the mantra, Srila Bhaktisiddhanta Sarasvati Thakura gives sixteen divisions, which are confirmed in the Hari-bhakti-vilasa (beginning with 1.204):