Bhakta-sanga means conversing with suddha–bhaktas (devotees performing pure devotional service to Lord Krishna), serving them, and hearing their discourses.  Suddha–bhaktas perform the activities of bhakti such as public congregational chanting of sri-nama.  Participation in these activities or performing them on one’s own is called bhakti-kriya-sanga, contact with acts of devotion. 

 In the scriptures, activities such as cleansing the temple of Sri Hari, offering a lamp to Tulasi, and observing Hari-vasara (Ekadasi, Janmastami, Rama-navami, and other such days) are called bhakti kriya.  Even if one performs them accidentally or without pure faith, they still create virtue that nourishes devotion.  When this sukrti acquires strength after many lifetimes, sraddha, faith for sadhu-sanga and ananya-bhakti (exclusive devotion) develops. 

It must be acknowledged that every vastu, substance, has some particular potency, which is known as vastu-sakti, the inherent potency of that substance.  The potency to nourish bhakti is found only within the activities of bhakti.  These activities produce sukrti even if they are performed indifferently, what to speak when they are being performed with faith.  This is expressed in the Prabhasakhanda quoted in Hari-bhakti-vilasa (11.451):

“Sri-Krishna nama is the sweetest among all things that are sweet, and it stands supreme amongst all that is auspicious.  It is the eternal, fully ripened spiritual fruit of the wish fulfilling tree of the Vedas.  O best of the Bhrgus, if anyone even once offenselessly chants Sri-Krishna Nama, either with faith or indifference, Sri -Krishna Nama immediately delivers that person from the ocean of material existence.” 

Thus, all types of sukrti that nourish bhakti are nitya-sukrti.  When this sukrti becomes strong, one gradually develops sraddha in unalloyed bhakti, and one attains sadhu-sanga.   

Birth in a Jewish/Christain/Muslim family is the result of naimittika-duskrti, or temporary impious deeds, whereas faith in ananya-bhakti is the result of nitya-sukrti, eternal pious deeds.   

If there is such a thing as bhakti-posaka-sukrti (virtue that nourishes devotion), it must arise from some other type of sukrti.  However, Muslims do not have any other type of sukrti, so it is not possible for them to have bhakti-posaka-sukrti either. 

That is not a fact.  Nitya-sukrti and naimittika-sukrti are classified separately, so they do not depend on one another.  Once there was a sinful hunter who was full of impious deeds, but who chanced to stay up all night and fast on Siva-ratri.  Because of the nitya-sukrti he accrued from this, he developed eligibility for hari-bhakti.  It is said in the Srimad-Bhagavatam (12.13.16):  

“Among Vaisnavas, Sivaji is the bes

From this statement, it is understood that Mahat.”   deva is the most Worshipful Vaisnava and one obtains hari-bhakti by observing a vow to please him.