Stick with it, there are rewards, if one of your homeless friends cooks you a meal or takes you out for your birthday or even lends you money then I think you can re-evaluate this 'helping' thing.
Also try and do things with money more as personal philanthropy, not through a structured charity. You would be surprised at how that works out. People do get back on their feet at they do pay you back. It can be important for them to do so because you were that person there for them when nobody else was.
It is possible to be white, male, cis-gendered, educated, able to earn money and still be treated as a world citizen. Intellect is universally appreciated, but it has to come with listening and willingness. People of all walks of life from all over the globe should be able to sense a happiness and peace that you have deep within, to get this within seconds of meeting you.
You could be spending your time with the upwardly mobile, going places crowd. Or you could give up your time to be best buddies with that elderly guy who can't remember what he did two minutes ago. Or some homeless local. In normal upwardly mobile society that would be a shameful thing to do - waste time on the 'weak'. Your rotten coworkers are stuck in this paradigm.
So you have to do things for your own motivations and ignore the crowd. There also has to be some reward in it for you. Seeing someone get their health back and their sense of being back is pretty good, particularly if you can look back on it and not be able to take any credit, with them having done it all themselves. Same in the educational setting, you should be able to reflect and realise they did whatever it was.
There is a difference between 'help' and 'enabling'. Receiving is also important, if your homeless buddy makes you something or pays you back (when some random grandparent dies) then that is more like it. Obviously you cannot take gifts from senile old folk because they don't know what they are doing!!!
Sometimes the personal philanthropy budget can grow rather than shrink. This is not a given, but people do get insurance payouts, fluffy animals can turn out to be insured and people do move on in their lives to not need the same material stuff. The more audacious you are with transformative sums with zero strings attached then the more likely it is that you will get calls out the blue with random Christmasesque paybacks.
You talk of feeling depressed and lonely, if you were to be realistic about the world then you could think that this is actually a fair and realistic sentiment.
I think you will feel a lot happier if you move from formal charity things to personal philanthropy projects. Long term commitment to two people at a time is more the idea rather than turning up once a year at Christmas time to dole out sub standard food to the 'less fortunate'. (Not saying you do that conscience-buying charidy thing).
Right now you could take on some co-worker's loser teenage child and give them some data entry work and the space to grow a bit. Give it time and they could be the child your co-worker is most proud of, to go on to get the exams and everything. With one of your homeless buddies you could put together a single page website for their dog walking business, doing the SEO and picking up useful skills in design that would not be allowed in the day job. Just apply the hacker mentality.