The political views of a far-right politician such as Höcke (probably aka Landolf Ladig[1]), if you translate them into what he hopes to turn Germany into, threaten the liberal democratic basis of the German constitution. And that we have a law against.
Naturally, the means through which said anti-nuclear activists try to achieve their goals, if only of making themselves heard, need to be legal, and if those actions are sufficiently illegal that they constitute a crime, I'm sure that will get the perpetrators in trouble and rightly so.
[1] https://andreaskemper.wordpress.com/2016/01/09/landolf-ladig...
http://www.dw.com/en/clashes-between-police-and-anti-nuclear...
A considerable part of their actions is very disruptive, seeking to, in the view of the protesters, I imagine, annoy everybody involved in the transport of nuclear waste to such an extent that they'll give up, while in actuality just causing a financial burden for the taxpayer (17000(!) policemen were in service during the protest you linked to according to [1]). That includes the traditional "Schottern" (the "[removal of] gravel from the bed of the train tracks to stop the train" as the article calls it), see also [2].
Even encouraging others to go "Schottern" on the internet is punishable[3] (sorry, again only in German) and punished, though.
And with respect to physical attacks, I think those protesters are rather harmless. I believe not a single policeman was injured in the aforementioned protests, even though thousands of protests were there (1500 at some point, 5000 at another point in time).
[1] http://www.zeit.de/politik/deutschland/2010-11/castor-gorleb... [2] https://de.wikipedia.org/wiki/Schottern [3] http://www.oberlandesgericht-celle.niedersachsen.de/portal/l...
http://www.focus.de/politik/deutschland/atomausstieg/castor-...
Anyway, I think that based on this it is not entirely unreasonable that the police does keep an eye on the protesters.
However, I'm quite doubtful about the wisdom of the "Trojan" plan:
http://www.dw.com/en/german-government-to-use-trojan-spyware...
If I recall correctly (well, this is from 2011), the majority of injured police was not at the hands of protesters but accidents, exhaustion and "friendly fire" - but a very few police got attacked or were injured in brawls and suffered minor injuries - the paramedics were mistakenly pepper sprayed by the police, and the police vehicles mostly had accidents where they drove into ditches and such, but a one or two were e.g. scrapped or damaged by people throwing train track gravel at it. Both injuries and damage (to police property), were aggravated by heavy rain and storm and the events taking place in rural areas and/or on gravel train tracks.
According to the police itself, most protesters were strictly peaceful and caused property damage to the train tracks at most ("Schottern").
So you got it mostly wrong, I'm afraid.
I do think it is extremely unreasonable and actually harmful to democracy for the police to track lawful, non-violent peaceful protesters exercising their basic rights (Grundgesetz) of free speech and freedom of assembly, or sanction or discourage them otherwise. This does not include violent people or people breaking the laws by e.g. willfully causing property damage, of course.
I also think it's very wrong to sanction people who you claim to be racist. If they are found to be unlawfully racist by an actual court, or demonstratively found to spread racist garbage as a teacher at a school, then again, that's a different matter.
My understanding of the demonstrations is that they were not intended as lawful, non-violent peaceful protests. The organizers wanted to make criminal damage (the "Shottern"), and some of the group were also very intent on violence.
The problem here is that anyone who was participating surely must have known what they're about to participate, even if many have themselves only wanted to not damage or hit anyone themselves. Just create a crowd where this can be done. And it is indeed hard to decide what level of surveillance is necessary and appropriate to prevent violence and large-scale damage.
(1) That's fair to do, but something to keep in mind when interpreting the numbers.
There's certainly a debate to be had about whether they're too strict, but IMHO, Höcke is so far across the line that I'm all in favor of keeping him out.
Edit: Note: higher standards apply for all government employees, but they're stricter for some, among them teachers, police etc.
Interestingly this list also contains the leftist party "Die Linke" which now has been a member of the federal parliament for a rather long time. That being said it's probably not a hindrance if you are a member there but you are expected to explain yourself.