Yup, you can definitely use orange EO instead of d-limonene, but you have to use about 15% more to get the same amount of limonene for equal cleaning power. But it is certainly worth a cost comparison, as well as a scent comparison, i.e., one person may prefer the scent of one over the other.
I first learned about using d-limonene in hand soap from the Swift Crafty Monkey blog, which is a very respectable source for safe use of ingredients. If you are a subscriber, you can read her
liquid scrubby hand soap formula here; it includes d-limonene at
~.7% - edited to add actual percentage from my notes of this recipe. Many of the "orange cleaners" used to wash greasy hands in mechanic shops use a combination of orange scent and d-limonene, but obviously I don't know the percentages they use.
Both orange EO and d-limonene can cause skin sensitivity, including phototoxicity. However, the amount of either that is used in hard bar soap is so low, and it is washed off so quickly, that chances of irritation are much lower than using either in say, a lotion or bath bombs, or even liquid soap.
If it were otherwise, we would not see all those mechanics using this kind of product daily on their hands.
. Our mechanic swears by my version of Earlene's blacksmith soap, which is my regular bar soap recipe with borax, pumice, and d-limonene. He says it is much gentler than the orange cleaner stuff that he used to buy, and his skin doesn't get irritated at all - just nice and clean.