Devanagari:
अधर्माभिभवात्कृष्ण प्रदुष्यन्ति कुलस्त्रियः।
स्त्रीषु दुष्टासु वार्ष्णेय जायते वर्णसङ्करः॥१.४१॥
दोषैरेतैः कुलघ्नानां वर्णसङ्करकारकैः।
उत्साद्यन्ते जातिधर्माः कुलधर्माश्च शाश्वताः॥४२॥
adharmābhibhavāt kṛṣṇa pradruṣyanti kula-striyaḥ
strīṣu duṣṭāsu vārṣṇeya jāyate varṇa-saṅkaraḥ
doṣair etaiḥ kula-ghnānāṁ varṇa-saṅkara-kārakaiḥ
utsādyante jāti-dharmāḥ kula-dharmāś ca śāśvatāḥ
adharma-abhibhavāt — from the prevalence of irreligion
kṛṣṇa — O Krishna
pradruṣyanti — become corrupted
kula-striyaḥ — the women of the family
strīṣu — when women
duṣṭāsu — are corrupted
vārṣṇeya — O descendant of Vṛṣṇi
jāyate — is born
varṇa-saṅkaraḥ — confusion of castes (literally "mixing of caste/racemixed")
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doṣaiḥ — by such faults
etaiḥ — all these
kula-ghnānām — of the destroyers of the family
varṇa-saṅkara — unwanted children (mixed race)
kārakaiḥ — by the doers
utsādyante — are devastated
jāti-dharmāḥ — community soul
kula-dharmāḥ — family soul
ca — also
śāśvatāḥ — eternal
"When irreligion prevails, O Krishna, the women of the family become corrupted; and when women are corrupted, O descendant of Vṛṣṇi, the mixed race arises."
"Due to the evil deeds of these family destroyers, the birthers of the mixed race, all of the eternal community and family religion / race soul are destroyed."
Arjuna is arguing against war:
War destroys families → family traditions / gemeinschaft (kula-dharma) perish
When dharma perishes, women become unprotected and "corrupted"
This leads to varṇa-saṅkara — race mixing
This mixing brings ruin to the soul of the family, the community (volksgemeinschaft / rasse-seele) and its ancestors
The social fabric will rot if he fights. The word śāśvatāḥ ("eternal") is significant—Arjuna is arguing that these family and social traditions are perpetual institutions (sanātana-dharma), linked to race, and their destruction is catastrophic