The AFD may be unappetizing, it may address ugly base instincts and sentiments in the population, but as far as I can see, it is NOT a Nazi party (which doesn't exclude the possibility that individual party members are influenced by far-right thought).
The AFD leadership in the state of Saarland had ties to genuine neo-Nazis; the AFD party convention decided by majority to throw them all out of the party and to dissolve the party in that state.
That party is heterogenous, and certainly "right-wing", encompassing different wings, including one "national-conservative" one with ties to the "New Right" and "Identitarian Movement", but they've made pretty clear and they have been rather vocal about respecting the constitutional order. The German Verfassungsschutz (Office for the Protection of the Constitution, a kind of "German NSA") at the moment sees no reason to observe the party.
For the record: I don't sympathize with the AFD, I'd rather see it not being successful, and I most certainly won't vote for it.
But a democratic attitude requires respect for political opponents, as long as they respect the constitutional order. Someone you politically disagree with is an opponent, not an enemy.
I feel many on the left are lacking this respect when it comes to the AFD: Everybody who disagrees with them is immediately labelled "a Nazi" or "neo-liberal" or both. These words are too often thrown around as mere slurs, and thus have lost most of their meaning. Newsflash for lefties: There are conservative opinions to the right of the center which do not violate the values of the constitution. If you want respect for your side, you have to pay the same respect to your opponents.
Also, these smears and slurs against the AFD are not just inappropriate, they are also totally counter-productive: It's basically free advertisement for the AFD. The "Nazi sledghammer" doesn't work anymore, most people even develop a kneejerk reaction *against* those who use it, just because it is often swung so inappropriately to smear opponents.
So if we want to keep the AFD small, singling them out and badmouthing won't work, it will only make them stronger. It's too late for that. It's better to address their stances and find arguments and reasons against them, and pointing out why they are bad ideas, whenever they are.
How about pointing out that a significant part of the AFD members want to leave NATO, and flirt with Putin's fascist dictatorship in Russia?
Or explain to lower middle-class and unemployed voters, who used to vote left, that the AFD ideas on economic policies favor big corporations and rich people?
It should also be pointed out that the AFD opposes equality of the genders by emphasizing "traditional families" and by their hateful rants against "genderism" -- they want women back into the kitchen. People interested in freedom for gay and queer people should also know the AFD is strictly against more rights for homosexuals.
Their stances give reason for criticism and counter-arguments enough -- no need to "play the Nazi card" on them, which has become a kind of "crying wolf syndrome" anyway.