The heilege Admor of Shaputnik, Moreinu v’Rabeinu HaGaon Shloimile Rosenbaum, of Tzfas, shlita, has commented on this issue in his sefer “Chalav u’Dvash.” He writes that one should be makpid NOT to cover the indoor table with a tablecloth, as one who is serving fleishig meals might, chv”sh, put a fleishig pot or plate on a milchig tablecloth that might be on the table in error.
The Shaptzniker, shlita, also mentions that we are noheig to serve fleishigs on Yontof, and refers to those who serve milchigs, r”l, as people who obviously do not follow the derech of their ancestors.