ये यथा मां प्रपद्यन्ते तांस्तथैव भजाम्यहम्।मम वर्त्मानुवर्तन्ते मनुष्याः पार्थ सर्वशः॥
ye yathā māṃ prapadyante tāns tathaiva bhajāmyahammama vartmānuvartante manuṣyāḥ pārtha sarvaśaḥ
Word by word
The verse says
However people come to me, that is how I meet them. Everyone follows my path, Arjuna, in every way.
In plain words
One of the most generous lines in the book, and it works by reflection.
Ye yathā māṁ prapadyante, tāṁs tathaiva bhajāmi - as they approach me, so I meet them.
Not they must approach correctly. However they come.
Where you've felt this · in parenting
Your mother has four children and is recognisably a different person with each of them. She is not being inconsistent. Each child found a different door into her, and all four doors were real.
Going deeper
The reciprocity here is exact, and it runs in both directions - which is unusual for a deity.
The verb is bhajāmi, the root of bhakti. It means to share in, to partake, to be devoted to. So the line is not I respond to them. It is closer to I am devoted to them in the way they are devoted to me.
The second half is harder and has been read two ways. Mama vartmānuvartante manuṣyāḥ sarvaśaḥ - people follow my path in every way. One reading: all paths eventually lead here. Another: everything people do is already happening inside what I am, whether they know it or not.
Both are held in the traditions and this edition does not choose. What they share is a refusal to make the door narrow.
It is also worth noticing where this sits. Three verses ago Krishna was destroying wrongdoers age after age. Here he meets everyone as they come. The Gita is content to hold both and does not smooth the edge between them.