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Controlling the spread of COVID-19 -- even after a licensed vaccine is available -- requires the effective use of non-pharmaceutical interventions, e.g., physical distancing, limits on group sizes, mask wearing, etc. To date, such interventions have not been uniformly and\or systematically implemented across the United States of America (US). For example, even when under strict stay-at-home orders, numerous jurisdictions in the US granted exceptions and\slash or were in close proximity to locations with entirely different regulations in place. Here, we investigate the impact of such geographic inconsistencies in epidemic control policies by coupling high-resolution mobility and search data to a mathematical model of SARS-CoV-2 transmission. Our results show that while stay-at-home orders decrease contacts in most areas of the US, some specific activities and venues often see an increase in attendance. Indeed, over the month of March 2020, between 10 and 30% of churches in the US saw increases in attendance; even as the total number of visits to churches declined nationally.  This heterogeneity, where certain venues see substantial increases in attendance while others close, suggests that closure can cause individuals to find an open venue, even if that requires longer-distance travel. And, indeed, the average distance travelled to churches in the US rose by 13\% over the same period, and over the summer, churches with more than 50 average weekly visitors saw an increase of 81% in distance visitors had to travel to attend. Strikingly, our mathematical model reveals that, across a broad range of model parameters, partial measures can often be worse than no measures at all. In the most severe cases, individuals not complying with policies by traveling to neighboring jurisdictions can create epidemics when the outbreak would otherwise have been contained. Taken together, our data analysis of nearly 120 million church visitors across 184,677 churches, 14 million grocery visitors across 7,662 grocery stores, and 13.5 million gym visitors across 5483 gyms, and modeling results highlight the potential unintended consequences of inconsistent epidemic control policies and stress the importance of balancing the societal needs of a population with the risk of an outbreak growing into a large epidemic.