That USMC Jersey is not an official Marine Uniform nor are any of the Services cycling jerseys. They are a depiction of the different branches of the military and as such, anyone can wear them. They are honorific in nature and not necessarily mean you are disrespecting any of the Services.
Now if you go out and purchase an actual uniform or a reasonable facsimile thereof and have never been in any of the services, you will get called out by those that have served. It is part of our job to make sure that active duty service members are wearing the uniform properly. And if an NCO or SNCO sees anyone wearing the uniform the wrong way, get ready for an ass chewing the likes of which you've never seen. We can usually spot uniform violations a mile away and an impersonator almost always makes a mistake.
Just be prepared to answer questions by those who usually don't know any better. A service member usually knows better, we usually just make a comment like, "nice jersey" or something along those lines.