If a 501(c) organization in its Articles of Incorporation state that its specific purpose is to aid homeless veterans, is it legal for them to use funds collected either solicited or unsolicited, to aid homeless that are not veterans?

Srictly speaking, I guess that would be ultra vires, but I question who would have standing to object. It is probably a non-profit corporation; if so a member could. Since it is a 501 (c) organization, the I.R.S. might too. Donors as well, probably.

They will need to inform all parties, esp donors that this will be done. A veteran donating money may feel he was cheated or there was a fraud, if they give money to help veterans and then the money is not used for that. They risk legal trouble for doing so.