Why don't I address your comment piecemeal? I'm going to assume that the thing we care about the most is poverty when we're talking about under privileged people.
> If in America, your options are very limited
How are your options limited? The US has over 1 million nonprofit public charities plus 400,000 other nonprofit organizations (foundations, civic leagues, etc)[1]. 62 million Americans volunteered for nonprofit work in 2015[2]. Americans give over $250 billion a year to nonprofits, about half to religious and the other half to secular[3]. None of this giving goes to government organizations, although of course some nonprofits get federal or state funding (probably a small %). But the point is that millions of Americans find a way to help the underprivileged apolitically--that is, there is little government intervention in their giving or how the money is spent.
> the answer very simple
The answer is clearly not very simple. Poverty is not only globally prevalent, it has never been eradicated by any historical or modern society, ever. If the answer was simple, someone would have solved it. Certainly a 'modern safety net' such as it may be defined by you or by others, open to interpretation as it might be, has been tried in many countries with mixed results. France, for example, has a robust public safety net and yet boasts a poverty rate of 14%[4] (the US official rate is 12% but to be fair these numbers might be apples and oranges[5]). In any event there is significant debate about the effectiveness of top-down poverty alleviation programs or about the form in which they may take. For example, many people now advocate UBI which is a far cry from the traditional notion of a public safety net but would replace it nonetheless.
> Use your money, time, voice and vote to support a modern public safety net.
I assumed by this you meant support a political party committed to expanding the public safety net, which in reality would be the Democratic Party, but it could be literally any party, the problems are the same. I suppose you could mean volunteer more taxes to the IRS, which is certainly an indirect option to filter some % of your donation to poverty alleviation programs, but I doubt you have done that or would expect others to.
I simply don't understand how giving your money to the Democratic Party, or any other political party, is supposed to improve their odds of winning an election, let alone using their elective power to improve social safety net. Obviously money doesn't buy elections--talk to Hillary Clinton or Meg Whitman about this one. And the last time Democrats touched the welfare system under Clinton they shrunk it and didn't expand it.[6] When Democrats last had both houses and the presidency from 2008-2010 they used their political influence to pass Obamacare, American Recovery and Reinvestment Act, and Dodd-Frank, all of which didn't address the public safety net except tangentially (you could argue, for example, that Obamacare / stimulus / financial reform indirectly help the poor but that's certainly debatable). There simply is no equivalence between the Democratic Party and actual results in helping alleviate poverty. In fact, the opposite may be true. Democrats have had, for years, one-party control of California, a state with the highest poverty rate in the nation (20%).[7] They also have had, for decades, a monopoly on power in the following cities which hasn't affected their poverty rates: Baltimore (24% poverty rate), San Francisco (13.8%), Detroit (35%), Seattle (14.5%)...the correlation between progressive politics and results on poverty alleviation is at best unclear.
> Every other avenue is a divergence or distraction or otherwise ineffective
It seems to me that any effort to fight poverty through political means is extremely indirect. The $1 you spend on, for example, campaign contributions, is going to pay to win an election first, and only if the election is won (which has little to do with your donation) you might get your new representative to sponsor a bill that would redirect strained government funds into expanding the public safety net. But of course such a bill would go through multiple committees and subcommittees, negotiations with real estate developers, unions, CEOs, nonprofit boards, and every dollar allocated will be subject to a myriad of political considerations, special favors allocated, slush funds established, and more. It will take years for your $1 to make its way into the pocket of someone who needs it in whichever form your elected representatives find most appropriate.
Whereas if you give that same $1 to your local homeless shelter it buys toothpaste for a homeless person who needs it and gets it tonight.
Why would $1 to a political campaign be more effective helping the poor than $1 given to an actual organization that spends 100% of their time helping the poor rather than trying to win elections?
> It is, however, obviously, politics. How could it not be?
I hope I've shown that politics is probably the most inefficient method your time and money could be used to help the poor, and that helping the poor can be done effectively without touching politics.
[1]http://nccs.urban.org/data-statistics/quick-facts-about-nonp...
[2]https://www.bls.gov/news.release/volun.nr0.htm
[3]http://nccs.urban.org/data-statistics/charitable-giving-amer...
[4]https://www.thelocal.fr/20160907/over-14-percent-of-the-fren...
[5]https://poverty.ucdavis.edu/faq/what-current-poverty-rate-un...
[6]https://en.wikipedia.org/wiki/Personal_Responsibility_and_Wo...
[7]http://www.politifact.com/california/statements/2017/jan/20/...