Dear Renu,
Many vaishnavites pray ONLY Lord Narayana but all the saivites pray Lord Shiva and Lord Narayana. I have one very
close friend ( Iyengar ) who has taken 'samAshrayanam' from her Guru and so she will not drink even water offered by me!
She will eat only fruits if offered by other vishanavite friends. Once upon a time, when I moved to this colony in 1984, she
used to prepare 'naivEdhyam' for Lord Ganesha, in our colony temple. But now she doesn't even enter that temple!
So, you can not expect any Lakshmi Narayana devotee to wear 'Namah Shivaya' shawl, in South India!
Vaishanvas consider Shiva as a great yogic divinity and a mAnasa-Putra, born out of the mind of Brahma. But, Shiva is not the antaryAmi of all creation, neither he nor Braham
can be supersoul of all jivAs/Creation, though they are highly realaized and powerful.
But, Shiva will grant excellent 'material' boons after a simple prayer/request, whereas Vishnu would grant such boons, but lead to unattachment. As main goal
of Vaishnavas is to attain that mOksha (not just the clarity of mind, but liberate and service afterwards), so they fear any worship or prayers to Graceful Shiva. So,
they just salute Shiva.
Plus, Shiva and Durga were the designated gods of those asuras, demons, forest dwellers who just want to achieve things/powers/positions , rather any realization.
Earlier Brahmans/sages insisted on the worship of Vishnu and only for realization, they were challenged by those materialistic kshatriyas/kings and later Brahmins
joined the fray.
There is no conflict in worshipping Shiva, but with the intent of realization, values, virtues. But, people have come up with scarier forms of worship to Shiva and Durga,
which you may have encountered in Kumbh mEla. Here, the real idea of sAttiva tenets are lost, as the philosophy and direction gets diluted!