Traditionally, the Setu is significant for Tamil clans around that area. In India the dominant clan is called Sethu-Pathy .. Tamil Kings in Jaffna called themselves Sethu-Kavalar (protectors of Sethu). All due to their belief their Lord Rama had legitimised their rule/role. For more than 1000 years.
So it goes without saying that implications are beyond religion. It goes on to tradition and society as well.
Why DMK is adamant, no-one knows. I can't rule out foreign role in this.