Recent literature has seen a considerable uptick in *Differentially Private Natural Language Processing* (DP NLP). This includes DP text privatization, where potentially sensitive input texts are transformed under DP to achieve privatized output texts that ideally mask sensitive information *and* maintain original semantics. Despite continued work to address the open challenges in DP text privatization, there remains a scarcity of work addressing user perceptions of this technology, a crucial aspect which serves as the final barrier to practical adoption. In this work, we conduct a survey study with 721 laypersons around the globe, investigating how the factors of *scenario*, *data sensitivity*, *mechanism type*, and *reason for data collection* impact user preferences for text privatization. We learn that while all these factors play a role in influencing privacy decisions, users are highly sensitive to the utility and coherence of the private output texts. Our findings highlight the socio-technical factors that must be considered in the study of DP NLP, opening the door to further user-based investigations going forward.