Only if it wants to jeopardize its charitable tax exemption.  A 501(c)(3) charity is prohibited from participating in a political election at any level of government.  Donating to a political party would be considered an intervention in an election.  (See Ready Reference Page: “IRS Guidance Has Not Changed on Electioneering”).  If the IRS looked, it could impose a fine or completely revoke the exemption.

What you could do about it is another matter.  Assuming you are only a donor and not a voting member or trustee of the organization, the most you would have standing to do would be to complain to the IRS.  Unless you are talking about a huge amount of money (and probably even if you are), the IRS is not likely to do anything about it.  Your primary recourse is to walk away and give your contributions to a vets charity that does only what it says it was set up to do.