A powerful Massachusetts state representative apologized yesterday for comparing a proposal requiring State House lobbyists to wear identification badges to the tattoos branded on Holocaust victims. Representative John J. Binienda, a Worcester Democrat who has served in the Legislature since 1987, said he made an “inappropriate analogy’’ when he criticized the badge proposal.“No comparison can be made between the Nazi regime and a rules proposal made by members in good faith,’’ he said in a statement yesterday. “I apologize to the sponsors, as well as the people of Massachusetts for my words.’’The proposal requiring that lobbyists wear badges was pitched by House Republicans last week as a transparency measure, so that members of the public, the media, and lawmakers themselves would know which special interests were attempting to influence lawmaking.On Wednesday, Binienda, who heads the House Rules Committee, called the proposal “revolting’’ and went on to make the historical analogy.“Hitler, during the concentration camps, tattooed all of the Jewish people so he would know who was a Jew and who wasn’t, and that’s something that I just don’t go along with,’’ Binienda told State House News Service for an article posted yesterday.