Anti-Semitism certainly isn't a "thing of the past" of that one can be certain. While it may not be on the lips of most, at least in 'polite' company, it is very much there and bubbles up now and again. It is always interesting to watch it surface and just as interesting, watching those who rush in and claim it is a "tactic". I have seen all forms of anti-Semitism, from outright, in your face kinds to more clever, underhanded versions.
Today, we still see blood libels, though they are mostly directed at Israel and Israeli politicians. The ever present "Jews control XYZ" is still very common, though many simply switch out the word Jew for Zionist, and to the bigots, it magically is no longer anti-Semitism. But, IMO, perhaps the most persistent is the "Jews are more loyal to X (now Israel)" argument. In the past, Jews were capitalist dupes...in the Soviet Union, but communists and socialists (sometimes true, but not how it is used) in the Western World. Today, let a Jew disagree with a policy, and regardless of Israel's opinion, said Jew is a traitor and more loyal to Israel. And, G-d help that Jew if her/his opinion is the same or even similar to Israel, because then that is proof positive s/he is a disloyal traitor.
Like other forms of bigotry, anti-Semitism isn't always so cut and dried. It ranges from slights like "You are so generous for a Jew." to redefining anti-Semitism to include others, and sometimes even exclude Jews to complaining about anti-Semitism being "just as important as other bigotries, so why must we discuss it". Then there are the more nefarious rants coming from the likes of David Duke, Louis Farrakhan, and others. Of course, I would be remiss if I didn't mention the plethora of "The Jews/Israel did it" conspiracies which, like the rising of the sun, are always just over the horizon and just as predictable; everything from Gore's loss in Florida, to 9-11, to Sandy Hook!
Anti-Semitism will continued to be overlooked except in the most extreme of cases, and for some, they will continue to ignore, deride, dismiss, deflect, and even propagate anti-Semitism. Both sides of the aisle do it, but only one side pretends it isn't something which can "happen here."