Generally, pull-ups are needed for inputs, not for outputs, unless they're open collector outputs, or something like that. Is that the case?
Anyways, it shouldn't make any difference, as when the output is "open" the pull-ups should pull the output up, and when the output is low, it should drive both the pull-ups low, unless that's over the output current capabilities, which would be rare.
Better if you put a schematic of the whole thing.