In episode 53 of the Unprofessional podcast, Dave Wiskus, Lex Friedman, and John Gruber interrupt an otherwise-entertaining discussion about chain restaurants to display both their liberal biases and faulty reasoning.
They "boycott" (if only one person does it, I'd call it "choose not to eat at") restaurants that have announced cutbacks in employee hours to avoid triggering Obamacare obligations to provide health benefits. They repeat the already-debunked claim that McDonald's could afford to double employee pay by increasing prices by a mere 17%, and they assert without evidence that Papa Johns pizza, to take one example, could easily increase pizza prices enough to pay for employee health benefits because rich guys like Wiskus, Friedman, and Gruber would gladly pay the extra.
Problem one: if Papa John's could raise prices without losing many customers to other pizza places, other fast-food options, or just eating in more often, presumably they'd raise prices already. The essence of profit-maximization is that further increases in price would be unprofitable because the additional profit from the higher revenue from customers who stick with you is outweighed by the lower profit from the loss of revenue from customers who leave. This fundamental fact doesn't magically go away when the scenario includes the opportunity to raise your own costs as well.
Problem two: the assumption that a price increase of "only" 17% (estimated to be more like 25% if done properly) wouldn't result in substantial numbers of people eating elsewhere is a rich person's assumption. A Big Mac meal is listed as $5.69, so a single person would face a price increase of $0.97 (at 17%) to $1.42 (at 25%), while a family of four eating two Big Mac meals and two Happy Meals (4 pieces Chicken McNuggets at $2.99) would pay between $2.95 (at 17%) and $4.34 (at 25%) for that meal. One paper summarizes studies on demand elasticities for a variety of food choices. Estimates for "Food away from home" range from 0.23 to 1.76, with a mean of 0.81. That is, a 10% price increase would lead to an 8% decline in purchases of food away from home. But that's for the industry as a whole. Demand elasticity for an individual restaurant is likely to be substantially higher, well in excess of one, as many other restaurants offer similar choices. Fast-food restaurants, whose demographics likely include far more lower-income customers than higher-end restaurants, are likely to have higher demand elasticity than other choices for dining out.
So feel free to boycott any restaurant you like. Your decision won't change fundamental economic facts.