Worship and legitimate responsibilities toward family, society, and one's own well-being need not compete. Responsible religious life combines prayer, learning, and remembrance with fulfilling ordinary duties.
لَا صَرُورَةَ فِي الْإِسْلَامِ does not mean every person must marry immediately in every circumstance. Rulings on marriage and Hajj involve conditions and individual capacity; those details cannot be settled from this brief sentence alone.
The negative expression corrects an exaggerated idea: complete withdrawal from lawful human and social duties is not itself the definition of religious excellence.