Poppa, it depends on whether dogs are keilim. Rav Moshe has a teshuva which Rav Eliezer Melamed brings that they are keilim for petting and therefore not muktza. However, Shemirat Shabbat k’Chilkata is machmir. If the dog is a keli than gets the next lower level of tuma you have. For example, If you are an av (e.g. if you were in a Jewish cemetery) once you pet him he is a rishon. Someone else who pets him would become a sheni.
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