https://www.reddit.com/r/badeconomics/comments/5u8hjx/the_fiat_discussion_sticky_come_shoot_the_shit/ddt32wc/?context=3

in crowding out, gov spending increases the demand => price is below equilibrium so prices go up => quantity demanded goes down increased price of good/service decreases the quantity demanded by private sector

someone or the government donating money to a charity does not increase the cost of donating another dollar; donating a dollar always costs a dollar

Draco seems to think that crowding out only applies to supply and demand models. He neglects to acknowledge that "crowding out" is often used in reference to the provision of public goods.

This has been studied in several laboratory and field experiments. Two especially relevant examples for the discussion regarding the provision of charity are:

An experimental test of the crowding out hypothesis: The nature of beneficent behavior by Bolton and Katok (1996)

An extensively studied model of public goods provision implies that government donations to charity crowd out private donations dollar-for-dollar. Field studies fail to verify this result. Several analysts argue that the problem lies with the specification of donor preferences. We report on a new experiment that provides a direct test of donor preferences free of the strategic factors that can confound tests in the field, and in other experimental settings. Our method involves the dictator game. We find extensive but incomplete crowding out ± direct evidence that donor preferences are incorrectly specified by the standard model.

An Experimental Test of the Crowding Out Hypothesis, by Echkel, Grossman and Johnson (2005)

We report the results of laboratory experiments that examine whether third-party contributions crowd out private giving to charity. Subjects play a single dictator game with a charity as the recipient. The subject chooses his preferred charity from a list. There are four treatment combinations: two initial allocations and two frames. Initial allocations are either US $18 for the subject and US $2 for the charity, or US $15 and US $5, respectively, and the subject is then given the opportunity to allocate additional funds if desired. The decision frame is also varied to affect subjects' perceptions of the task. In one frame, subjects are simply informed of the initial allocations between themselves and their chosen charity. In the other, subjects are told that their US $20 allocation has been taxed, and the amount allocated to their chosen charity. The structure of payoffs is identical in both frames. In the first frame, we see a level of crowding out that is close to zero, far less than other experimental studies; in the second frame, we observe nearly 100% crowding out.

As we can see, experimental studies indeed suggest that government provision of charity may crowd out private provision. /r/libertarian is right!

A review of many other papers, and additional discussion of the theory can be found in Bowles Hwang.

More broadly, while "government donating money to a charity does not increase the cost of donating another dollar" is not looking at the whole picture:

1.) The government pays for these donations through taxation. Since there is less money available in the private sector, people have less money to spend.

2.) Assuming the government is applying charity to where it is most needed, the marginal benefit of private charity will decrease. Since MB=MC rational agents will donate less.