Historically, donations to charities drop when tax rates go down. As a percentage of income, donations were highest when tax rates were highest.
The best example that low tax rates don't increase giving: in 2017 the TCJA reduced tax rates for most people, and increased the standard deduction (but reduced the charitable deduction). Even though they were being taxed less and had more money to donate, Americans donated several billion less to charities each year (estimates very, but they're all between $15 and $20 billion less each year).
I want you to know I took some time research and educate myself on these claims.
From my findings, I could not find anything directly correlating the 2017 TCJA to total donations. The TCJA did change how deductions are treated, and more people opted to go with standard deductions instead of itemized deductions, but this is not the same as total donations. It is possible this incentivized people to donate less because they couldn't get as much of a tax write off.
For total donations, it has continued to trend upward despite some fluctuations, and a $20 billion swing is not a large deviation. The numbers I saw were $400+ billion during that time. Again, this has many more factors than the TCJA.
Most importantly, I'd like to reiterate that libertarians do not claim that cutting government will "solve" problems like open source projects getting enough funding. Just that it will give the free market an opportunity to find a balance. No big bill is going to solve these problems either, it will only make it worse. The end does not justify the mean. Stop taking people's money, and let them spend it on the things they find valuable even if you disagree with it.