Although cute, there is definitely a false equivalency. The real difference is that the "Conservative" argument is yes, it is their right in both situations, but how they handle it is different. One will simply voice their displeasure and stop patronizing a business, the other will use whatever means they can to punish the business through litigation, politicization, slander, vandalism, violence, or using the force of the government. If they do not get their way, they will do it again. Perhaps the better comparison would be adult vs. petulant child.
I think this is an example where the market should decide. If a business doesn't want the liability and they think that most of their customers would feel safer if everyone were wearing masks, then let the market decide. Maybe another competing business thinks there's a market for people who don't want to wear masks, so they don't have the rule. Let's see whose idea wins.