。
I don't feel ashamed of being poor.
Literal
Poor [copula-である] thing [object-を] shameful [quotative-と] do-not-think.
であること nominalizes the state of being poor. 恥ずかしいと思わない means 'don't think it's shameful,' with と marking the quoted thought. A dignified statement about not being ashamed of one's financial situation.