The most likely outcome of this situation would be that the two would get along as they recognize everyone's right to decide whom to worship.
Shivaism and Vishnuism are branches of Hinduism that are differentiated by the main God they worship, while Shivaism worships Shiva, Vishnuism worships Vishnu.
According to Hindu traditions, the different branches of Hinduism have no conflict with each other and recognize the right of others to worship whomever they prefer. Due to the above, their relationship would be good and they would only be differentiated by the God that each one adores.
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