Why do poor people vote for the benefit of a group of people whom they'll never be a part of?

I don't understand your question. What group are they voting for that they will never be a part of?

Charles Davis is correct in saying religion -- at least, in the US. (Religion has lost most of its influence in the majority of developed countries while America lies a good 50 or 60 years behind.)

The other factor is the ability of the spin doctors of both parties to control the information given to the voting public.

Not all the "poor people" of your question are uneducated or unintelligent but there's a tendency for people in lower-paid jobs to be there for that reason. That makes them fairly easy to manipulate.

Something else unique to the United States is the use of the word "liberal". In other countries it means progressive, or open to change. It's used by Republicans as a slur and, in their context, is as damning as "commie" or "pinko", each of which is also uniquely American.

The only solution is for average citizens to educate themselves on what's happening, step aside from the party politics of either side, and vote according to the issues.  That's much easier to do now that we can check any news stories against unbiased sources, as well as those that covertly support one party or the other.