Also, caving on free speech for international political reasons is still caving on free speech. Protecting people from such political calculations is the whole point of constitutional guarantees of free speech in the first place.
That law explicitly (and untypically) states that the executive has to decide that the district attorney may press charges, which was granted in this case. The law is stated as "the executive needs to authorise prosecution", but due to how it's structured (executive reigning in to a matter of court) it's really more of a veto. (http://www.gesetze-im-internet.de/englisch_stgb/englisch_stg... - section 104a is about the veto)
Then there's the rule that when laws change, the sentence is capped at the "mildest" legal result for the defendant between opening the case and the final verdict (to paraphrase things _very_ roughly, details at https://dejure.org/gesetze/StGB/2.html, in english at http://www.gesetze-im-internet.de/englisch_stgb/englisch_stg...).
So what could happen:
1. The executive (through Merkel) allowed the use of the law in this instance. At the same time, there's consensus within the executive and most of the legislative that the law should be repealed.
2. The jurisprudence opens the case, it drags on for a year. (or they decide not to take on the case, in which case everything stops here)
3. There's a verdict. Boehmermann can appeal several times, dragging this on for another 4 years or so.
4. At some point the law gets repealed.
5. The next time a court hears the case, they'll kick it out because there's no law and therefore there can be no prosecution.
An alternative reality might be:
1. The executive stopped prosecution under this law because they can.
2. We'd hear about how the German government stepped in on matters of jurisprudence every. single. time. that Germany complains about overreach and a lack of rule of law in Turkey (and probably elsewhere). A gift that keeps on giving.
Then there's also the more general defamation law (applicable to everybody and with no executive veto clause). Due to where the TV station is headquartered, the case is handled in Mainz. For those defamation cases, the Mainz district attorney has a rule that a mandatory mediation meeting must happen in person in Mainz, with no exceptions.
Not sure mediation is something Erdogan really wants to do for what is essentially a populist stunt.
Look at the enormous change in U.S. police prosecutions in the last couple of years due to public pressure. I seriously doubt the amount of misconduct drastically increased.
Though CaptainZapp's reply was low-signal, snarky, and redundant with her/his down vote, it did inspire me to learn more about German law.
It appears that by statute, German prosecutors have little discretion when it comes to pursuing convictable cases. They may only nonprosecute minor offenses, i.e. those with sentences of less than one year. However, there are exceptions that are applied by prosecutors that could apply to this case. One is the "serves the public interest" exception; another is the "may damage state interests" exception. Either way, the answer isn't cut and dry and contains way more nuance than my original comment and its reply suggest.
[1]. http://law.jrank.org/pages/1855/Prosecution-Comparative-Aspe...