This is why Congress passed the rules on unrelated business income and imposed the federal income tax on unrelated business taxable income.  The key question in this situation is the scope of operations for which the Humane Society has been granted exemption.  If it is exempt only to prevent cruelty to animals, these services to the public may be unrelated and subject to unrelated business income tax (UBIT). If it is exempt for broader purposes of providing such services for animals generally, the activity may not be unrelated. (See Ready Reference Page:  “Nonprofit Often Worry About UBIT”)

The competing vet may be able to obtain a copy of the Form 1023 application for recognition of exemption from the Society (See Ready Reference Page: “Tax Exempts Must Provide Applications, Returns”) or from the IRS.  If the individual vet has a problem, he or she might be able to file a complaint with the IRS, although I wouldn’t expect a whole lot of help.  If the vet is in Pennsylvania and the activity is unrelated, the vet may be able to obtain an injunction under the state’s Act 55, which defines a charity and permits small business to seek an injunction against certain unrelated business activities.  (See Ready Reference Page: “Act 55 Defines ‘Charity’ Eligible for Exemption”)