I've just tested this on 10.4.1 and a selection is honoured when one runs a project tool on a feature layer which has some features selected and only they get projected.
This idea has been closed as a duplicate of the Data Management Idea linked below. Don't worry, you can still show your support by commenting and adding kudos to the open idea. Thanks for your contributions!
https://community.esri.com/t5/data-management-ideas/project-should-respect-selections/idi-p/934729
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