I have a pink seedless grapefruit that still has fruit from last year hanging. Will that stop it from producing fruit this year??

It is normal for grapefruit and late-season oranges (e.g., 'Valencia') to carry two years' crops together in the late spring. But yes, the longer you leave the mature crop, the fewer of next year's fruit the tree is likely to carry to maturity. Still, grapefruit are so ridiculously productive that it usually doesn't matter.