NonCredibleDefense

The famines in India because of the British

Not capitalism, that was imperialist mercantilism (source):

Nightingale identified two types of famine: a grain famine and a "money famine". Money was drained from the peasant to the landlord, making it impossible for the peasant to procure food. Money that should have been made available to the producers of food via public works projects and jobs was instead diverted to other uses. Nightingale pointed out that money needed to combat famine was being diverted towards activities like paying for the British military effort in Afghanistan in 1878–80.

The British took money from peasants and used it to fight in Afghanistan. That sounds a lot like feudalism or mercantilism to me, not capitalism. Capitalism doesn't funnel money into war, governments and warlords do.

famines in Ireland

This one is much closer to capitalism:

The proximate cause of the famine was the infection of potato crops by blight (Phytophthora infestans) throughout Europe during the 1840s. Blight infection caused 100,000 deaths outside Ireland and influenced much of the unrest that culminated in European Revolutions of 1848. Longer-term reasons for the massive impact of this particular famine included the system of absentee landlordism and single-crop dependence. Initial limited but constructive government actions to alleviate famine distress were ended by a new Whig administration in London, which pursued a laissez-faire economic doctrine, but also because some in power believed in divine providence or that the Irish lacked moral character, with aid only resuming to some degree later.

Basically, it seems to have started with a colonial mindset (absentee landlordism) and transitioned rather abruptly to laissez-faire capitalism, with a backdrop of racism. Basically, Protestant supporters of Elizabeth 1 were granted a lot of land, and they rented that out to the Irish people. It's a bit more complicated than that, but it absolutely didn't start out as capitalism, it started out with grants from the monarch, and then during the famine, London transitioned to more laissez-faire policies, which basically just cemented the position of those large land-owners.

Laissez-faire capitalism can absolutely help longer term, but there needs to be enough time for more productive owners to beat out entrenched owners, and that's just not possible in a famine, and it certainly doesn't happen overnight. The way this would work is some natives would pool up enough money to buy land outright (or accept foreign investment to do so), improve it, and get more profit than the absentee land-owners who didn't care to invest in their properties (and the farmers didn't care to improve land they're merely renting). Once land is producing more, that would lead to excess and opportunities to invest elsewhere (e.g. factories).

Great Britain completely mismanaged things though, especially the transition from crown handouts to laissez-faire economic policy. So I think the biggest explanatory factor here is racism ("divine providence" or whatever).

Yes, the reasoning in both is to make money, but neither was operating under a proper capitalist system, since both operated under the thumb of British aristocrats. If you want to see what can happen when people throw off the aristocracy, create a stable government, and actually let laissez-faire capitalism work, look at the northern United States after independence from Great Britain. They abolished slavery and progressed the economy very rapidly, to the point where they could largely hold their own against the British in the war of 1812 less than 50 years later.

https://en.m.wikipedia.org/wiki/Banana_republic

This is state capitalism, which is closer to whatever China is than laissez-faire capitalism. It's pretty much textbook cronyism, since the only ones allowed to actually operate in the economy are cronies of the state.