It's hard to provide an objective answer since this is a question mostly about emotions and everyone has his anecdotes. Since pretty much all answers here do not have any citations or references, it's likely that they are all colored by subjective perception.
I'll try to provide some objective data, though it will undoubtedly still be colored by my personal opinion:
According to one poll from cicero questioning 2088 people:
Bei den Wählern der AfD sind die Zustimmungswerte für Trump mit 52,9 Prozent mit deutlichem Abstand am höchsten, am niedrigsten sind sie bei den Wählern von Bündnis90/Die Grünen (2,9 Prozent). 81 Prozent der befragten CDU/CSU-Wähler lehnen Trump ausdrücklich ab, ebenso wie 84,6 Prozent der befragten SPD-Wähler und 78,3 Prozent der FDP-Wähler. Bei den Wählern der Linkspartei sprachen sich hingegen lediglich 72,5 Prozent der Befragten ausdrücklich gegen Trump aus.
Demnach sehen 36,7 Prozent der Muslime den neuen US-Präsidenten positiv, bei den Katholiken hingegen nur 9,9 % und bei den Protestanten 11,3 Prozent. Weniger als die Hälfte der befragten Muslime (47,7 Prozent) lehnt Trump ausdrücklich ab; bei den Katholiken liegt dieser Wert bei 71,4 Prozent und bei den Protestanten bei 73,6 Prozent.
My translation, annotations about the parties in brackets are mine. Seats in the "Bundestag" (Parliament) from Wikipedia:
Of the voters, the approval rating among the AfD [far right party, 89 seats (12.6%)] voters are by far the highest with 52.9 percent. The lowest approval rating is among the voters of Bündnis90/Die Grünen [green party, 67 seats (9.4%)] (2.9 percent). 81 percent of the CDU/CSU [christian democrats, center right, 246 seats (34.7%)] explicitly refuse Trump, just like 84.6 percent of the SPD [social democrats, center left party, 152 seats (21.4%)] voters and 78.3 percent of the FDP [economic liberal party, 80 seats (11.3%)] voters. Among the voters of the Linkspartei [left party, 69 seats (9.7%)] only 72.5 percent refused Trump.
36.7 percent of the muslims view the US president positively, among the catholics only 9.9 percent and the protestants 11.3 percent. Less than 47.7 percent of the muslims explicitly reject Trump; among the catholics it's 71.4 percent and for the protestants 73.6 percent.
So in summary:
- The greens really dislike Trump
- Centrist parties, both left and right, are numerically his biggest opponents
- The isolationist, anti-EU AfD has the highest approval rating for Trump, but almost half of them still dislike him
So correlating from that data:
- Trump is disliked for his ecologic policies, mostly likely for rejecting the Paris accord and his stance on climate change
- Anti-refugee parties (AfD) approve of him more than pro-refugee parties (Everyone else, to some degree), so his stance on refugees and immigration is probably a factor
- Parties favoring stability (centrists) disagree more with him than parties that favor change, so his unusual behavior appears to be a point of contention among Germans, who tend to vote for centrist parties
I have difficulty figuring out reasons for the religious approval rating since his anti-muslim stance should lead to higher disapproval among muslims, but the opposite is the case. It should be noted however that religion in Germany plays a very minor role among Christians, especially outside of the state of Bavaria.
Taking another poll from YouGov for the DPA (Deutsche Presse Agentur/German Press Agency):
US-Präsident Donald Trump wird in Deutschland als größere Gefahr für den Weltfrieden wahrgenommen als Russlands Staatschef Wladimir Putin oder der nordkoreanische Machthaber Kim Jong Un. Nach einer Umfrage des Meinungsforschungsinstituts YouGov im Auftrag der Deutschen Presse-Agentur (DPA) wird Trump auch für gefährlicher gehalten als das politische und religiöse Oberhaupt des Irans, Ajatollah Ali Chamenei, und Chinas Präsident Xi Jinping.
41 Prozent der Befragten sagten, Trump sei von diesen fünf Persönlichkeiten die größte Gefahr für den Weltfrieden. 17 Prozent entschieden sich für Kim, jeweils 8 Prozent für Putin und Chamenei sowie 7 Prozent für Xi
Translation again mine
US president Donald Trump is viewed in Germany as a bigger danger for world peace than Russian president Vladimir Putin or the Northkorean Leader Kim Jong Un. In a Poll from YouGov for the Deutsche Presse-Agentur (DPA) Trump is viewed as more dangerous than the political and religios leader of Iran, Ajatolla Ali Chamenei, and Chinas president Xi jinping.
41 percent of the respondents answered that Trump was the biggest danger for world peace among those five leaders. 17 percent decided for Kim, 8 percent each for Putin and Chamenei and 7 percent for Xi
This leads me to the conclusion that his erratic behavior, combined with his power to actually mess up the world peace as the leader of the country with the biggest military, is viewed as very dangerous by Germans.
Justifying the poll results from my personal view:
Germany has been dealing closely with Vladimir Putin for years and we have good trade relations with China, so both are known factors and chances are that the future with them will be business as usual. Putin is a known evil, we don't trust him but we also know that he's as rational as it gets. Xi is interested in economic power and war is bad for trade, so while the human rights violations and the Taiwan situation are bad, he wont endanger world peace. Kim Jong Un has been blustering for a long time, but, while he could kill a lot of people, he's more interested in staying in power than starting a war, so he's unlikely to mess up world peace. Iran was under very close observation where nuclear technology was concerned, so, while they do plenty of unsavory stuff, they don't have the power to actually disrupt world peace. They cause regional instability, but that's pretty much all they can do. So while those four are bad and/or evil, they aren't world peace shattering bad.
With Trump, he has the power to really, really mess up world peace. His behavior is unpredictable, so we can't rely on him to not mess it up at some point. There is a lot of uncertainty in dealing with Trump, which makes Germans anxious.