* Soy shipments waning, sugar and corn picking up
* Drivers want diesel subsidy, no highway tolls
* Last year's strike had no impact on grain exports
SAO PAULO, June 28 (Reuters) - Brazil's trucking union is calling for a 72-hour strike starting on Monday, potentially slowing the movement of record soy, corn and sugar crops to ports, although unlikely to stop exports.
MUBC, as the most influential truckers union in Brazil is known, encouraged all sectors involved in transporting cargoes in the country to participate in a "passive protest" starting 6 a.m. (1000 GMT) on Monday, in a written statement posted online.
Threats of a general strike in Brazil, which saw its largest protests in 20 years last week over issues ranging from education to corruption in politics, are generally considered overblown, with pledges of participation waning.
The trucking union's demands include a subsidy for diesel fuel, exemption on highway toll payments for drivers and the creation of a new federal government department of cargo transportation.
The threats comes as the last of Brazil's record soybean harvest is on the way to the ports and traffic from sugar and corn crops is picking up. Unlike the United States, the western hemisphere's other grains powerhouse, Brazil relies overwhelmingly on trucks to move commodities and has not developed many trains or waterways.
The MUBC last went on strike for a week in July of 2012, disrupting the flow of goods in the country's heavily populated southeast and spurring fears of higher food prices.
The main ports of Paranagua and Santos did not report snags in the flow of bulk commodities to foreign markets and most exporting companies keep grains in private storage units to minimize the effect of interruptions to ground transport. (Reporting by Caroline Stauffer. Editing by Andre Grenon)