TLDR: Without political polarization and passionate public disagreements on court rulings, the German People do not really care about how judges are appointed, which enables the political parties to make simple deals.
The appointment procedure differs between the two legislative bodies:
Half of the members of the Federal Constitutional Court are elected by the Bundesrat, which is the legislative body representing the states, the other half by the Bundestag, the federal legislative body.
The members of the Bundesrat are not elected but appointed by the state governments. Since CDU and SPD, historically the biggest parties in Germany, for the longest time held the necessary 2/3 majority together, they made a simple deal: They simply take turns in appointing judges.
In the year 2016 however the Green Party gained enough members in the Bundesrat to block candidates, so they had to be included the deal.
The current rotation of appointments is: CDU - SPD - CDU - SPD - Green.
The Bundestag in turn forms a committee which negotiates a candidate that a necessary majority of parties can agree upon. The exact details of the negotiations within this committee aren't known and the final vote in the Bundestag is performed with secret ballots, which is why the whole appointment procedure is often criticized as intransparent.
It wouldn't be terribly surprising if there were secret dealings in a similar fashion to what happens in the Bundesrat, where a 2/3 party majority simply takes turns on appointing uncontroversial candidates.
The major reason for why the appointment of judges is usually a quiet and uncontroversial event, although there are certainly enough things that can be critized about the appointment procedures, is that there is no political split and polarization in Germany comparable to for example as in the US, where you have to deal with two judicial philosophies and two political parties that are vehemently at odds with each other.
While there have been controversial decisions by the Federal Constitutional Court, overall it is held in high esteem by the German People and is widely seen as functioning well.
If there were deep public disagreements about fundamental court rulings like Roe vs Wade in the US or polarization comparable to Democrats vs Republicans the appointment procedures would probably very quickly come under public scrutiny as well.
Since I already used the US as an example it should also be noted that multi-party-systems usually have far better relationships and cooperation between the respective parties than a two-party-system, since the parties have to enter coalitions to form a government, which makes appointments that require cross-party-cooperation significantly easier since the parties are used to working and cooperating with each other.