Does our society give too much leeway to people with companion pets?

I have seen several companion pets over the past week. In grocery stores and in restaurants especially. That got me thinking about our societies willingness to grant these people the right to drag their pets with them wherever they want to go. What about the rights of people that might have fear of dogs (or whatever other animal they have) and are trying to shop or eat at the same establishment? What about people that have bad allergies to these animals? Don’t they have the right to not be subjected to their allergy triggers? We worry about surrounding people when it comes to 2nd hand smoke but not when it comes to companion animals. Is there really a difference?