General case - legal or not?
It is hard to prove a negative - however, as far as I can see:
It is not illegal to state your opinion that the existence of the state of Israel is unjustified, or that the state should be dissolved.
Such a position would be considered outrageous by most Germans, in particular it is against the stated position of pretty much all political parties, except for the extreme right or left, and of most other organizations. It is not, however, illegal.
In general, the dissolution of a state is not in itself illegal according to national or international law, as long as it happens voluntarily. There are some precedents: For example, during the German Reunification of 1989, the German Democratic Republic (East Germany) acceded to the Federal Republic of Germany (West Germany) under the (old) Article 23 of the Grundgesetz. One could argue that the German Democratic Republic effectively dissolved itself by that accession.
What would probably be illegal would be to call for a violent end of the state of Israel, or even for a war. The relevant laws:
Special case - civil servants
Civil servants are citizens, too, so mostly the same laws apply to them. However, for civil servants specifically there are higher requirements when it comes to respect for the German constitution, specifically for the "freiheitliche demokratische Grundordnung" (literally: "basic free and democratic order"). That means that opinions which are "extremist" but not illegal may not be tolerated.
As far as I can see, the rules for whether something violates these rules would be similar as above.
Note that there are even some Israelis who think that the state of Israel should not exist, at least not in its present form, so such a position is not totally unthinkable. The Wikipedia articles Right to exist and Existenzrecht Israels (German) give a good overview.