Phil started the war with Tony. Breaking the rules in the commission of war is different than breaking them in peacetime. When Tony is at the diner with his family, an accord had already been reached between the Lupertazzi's and Sopranos. So, in that instance, killing someone right in front of their family would be less tolerable. When Soprano soldier Walden spotted Phil at the gas station, Phil was on the hunt for Tony. It's on site in a situation like that. Doesn't matter if Phil has the Pope with him.

"...the successful annihilation of organized crime's subculture in America would rock the 'legitimate' world's foundation, which would ultimately force fundamental social changes and redistributions of wealth and power in this country. Meyer Lansky's dream was to bond the two worlds together so that one could not survive without the other." - Dan E. Moldea