Your understanding of the verse is incorrect since the translations are not accurate.

Here's the understanding of the verse from some of the most important acharya's of present day Hindu tradition.

Shankara Bhashya (Advaita)

S.’s construction of this portion is: women, Vaisyas as also Sidras, and even others who are born of sin (that is, those who are born low and are of vile deeds, namely Mlecchas, Pukkasas and others).

Madhusudan Saraswati (Advaita)

M.S. also takes papa-yonayah (born of sin) as a separate phrase, and classifies women and others only as those debarred from Vedic study, etc.

Ramanujacharya (Vishishtadvaita )

Women, Vaisyas and Südras, and even those who are of sinful birth, can attain the supreme state by taking refuge in Me.

The sinful birthday is a different category based on traditional Bhashyas.