Does a seafarer travelling to Dubrovnik from Mumbai via Munich need a Transit visa?

According to the Schengen Visa Code:

Nationals of the third countries listed in Annex IV shall be required to hold an airport transit visa when passing through the international transit areas of airports situated on the territory of the Member States.

According to the German Embassy in India, Indian citizens also need to obtain an airport transit visa:

All Indian citizens in air transit through Germany need to apply for a transit visa at the Consulate General

There are several exemptions listed in the Visa Code, but none of them apply specifically to seafarers:

(a) holders of a valid uniform visa, national long-stay visa or residence permit issued by a Member State;

(b) third-country nationals holding the valid residence permits listed in Annex V issued by Andorra, Canada, Japan, San Marino or the United States of America guaranteeing the holder’s unconditional readmission;

(c) third-country nationals holding a valid visa for a Member State or for a State party to the Agreement on the European Economic Area of 2 May 1992, Canada, Japan or the United States of America, or when they return from those countries after having used the visa;

(d) family members of citizens of the Union as referred to in Article 1(2)(a);

(e) holders of diplomatic passports;

(f) flight crew members who are nationals of a contracting Party to the Chicago Convention on International Civil Aviation.

Unless you fall under one of the exemptions listed above, you will need to apply for a transit visa.