Would you agree that it is more important to feel like a Muslim rather than to just look like one?
Definitely. Religion is the spiritual part of life, mind, body, and soul have to agree. Especially with Islam, the basic laws of the religion are universal and Islam just put a name to them, a label if you will. If you dob't have the basis to committ yourself spiritually and decide to just look like a Muslim then you aren't really doing anything.