Depends on some factors:
A. Who pays the subsidy tax (depends on corruption)
C. Cutting taxes (or not) after reducing the subsidy.
A. If the (most of the) money for the subsidy tax is collected from the people with big revenues (from the rich), then the rich pay for cheaper fuel, helping the poor people to get cheaper commodities (food, clothes, etc). And that's not bad at all. And then, cutting the subsidy makes the food more expensive and that has a negative impact on the many.
But if the money for the subsidy is collected from the average citizen and and from the poor, then the poor will pay for slightly cheaper food but also for cheaper fuel for the rich who want to enjoy car/airplane trips for pleasure. Because not all the subsidized fuel is used for transporting commodities - a part of it is used for personal cars/taxi/airplane for enjoying a good time. That means that not all the money paid in subsidy return in cheaper food for the many. In this case, cutting the subsidy (and subsequently reducing the tax for the subsidy — (C.)) will have a beneficial effect—the average citizen will not pay a tax that doesn't return entirely back to him.
B. Example: Brian Jones has to pay \$10 US in fuel subsidy tax. The owner of the truck transporting the food from the producer to the supermarket will pay \$10 less in fuel expenses (say \$90 instead of \$100). The supermarket will get the food for \$10 less and it will sell with \$10 less. Brian Jones goes to the supermarket and buys all that food for \$10 less. In the end, Brian Jones pays \$10 but he gets \$10 back. So if the average citizen pays the subsidy then, in the best case, there is no benefit at all.
The problem is:
Not all the subsidized fuel is used for transporting basic goods. Therefore only a part of the subsidy will return in cheaper goods.
The distribution company and the supermarket won't price the products for 10 \$US less. Instead of providing cheaper goods/services, they will increase their profits. They will make all that food just 5 \$US cheaper or even for just 1 \$US cheaper, and the rest of 5 \$US or 9 \$US will be used to increase their profits.
If the government is corrupt, the Competition Council will not do it's job and it will allow this. That's what happens in most of the poor and corrupt countries.
In a country with a corrupt government, the food will be more expensive than say in France, even with free fuel. Because the small producers can't sell directly to the consumer—they have to sell to monopolies/cartels/mafias of distribution companies or supermarkets that artificially inflate the prices.
For example a man from Philippines working in Denmark told me that most of the food is two or three times more expensive in Philippines than in Denmark. Even rice is much more expensive, although the country is a rice exporter. Also the fuel is more expensive. This is by far the biggest impact of corruption on the people everywhere in this world - consumers get overpriced goods.
To have an idea, in Spain a kilogram of rice costs 0.65 Euro, a kilogram of sugar - 0.65 Euro, a liter of sunflower oil - 1.20 Euro. In Indonesia should be much cheaper because the workers wages are much lower. But most likely it's not cheaper, maybe it's even more expensive to buy such things.
Considering all the above, now we can give the short answer:
- The government reduces a subsidy paid by the rich and that increase the price of food. OR
- The government reduces a subsidy paid by the poor, that increases the price of the food, but the government doesn't return the subsidy to the poor in tax cuts (no subsidy, no tax for subsidy). OR
- The government reduces a subsidy paid by the poor, returns the money to the poor by cutting their taxes, but in the same time it allows the cartels/monopoly to further artificially increase the price of the food, and then blames the reducing of fuel subsidy for increasing the food price.
So in the end this is all about corruption. Cutting the subsidy serves just as an excuse. The negative effect comes because of the corruption not because of reducing subsidies.
I think however that such questions better fit on a Q&A site about corruption/society than on a site about economy.