I think it is a "middle school Pissing contest", (boys in the field will test the distance). It is too childish.
Who has seen Vishnu or Shiva? These differences are purely man made. Fortunately for younger generations it does not seem to make any difference. Two of my nephews are married into Iyyangar family. At least we are still cordial when we meet. The kids in the family are all named a mix of shavite, vaisnavaite, or other names. Most of the Hindu temples in North America have Shiva, Vishnu, Devi, ganesh, mahavir jain, Iyyappa, and some I do not even understand.
There is XXXXX Temple in New York, which was built as strict Iyyangar Temple. The temple had draconian rules. Women were not allowed in Kitchen, only ordained priests were allowed. The place is so run down and dirty that health department had to close the kitchen. The priests brought from India refused to clean the floors. The priests would use shawl to cover their upper body against the rules. (it is cold with snow on the ground).
The Vardraja Temple is run by Shankar Mattam in Kanjipuram.
Who really cares about some personal quirks, codified into rules by some forgotten person long ago.
I have a cousin who was some big shot in TVS, and was able to get the MD of TVS group to participate in kumbashikam for a shiva Temple. Money Talks.
The same person goes even to Sri-Rangam temple with lot of Vibhuti on his forehead, and gets special privileges because he knows the devestanam board member who accompanied us.
It all connection and money that speaks loudly than any prescribed rules.