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I want to freelance part time for a product I love would that conflict with where I am currently employed?
Only if its a direct competitor!
It all depends if it conflicts with your company's policies.
Check your orgs moonlighting policy. I freelance promoting products my company develops. As long as I dont leverage my position or use my company equipment to make side money, I'm good. My clients dont know who I work for unless they creep on my LinkedIn.