I am interested in the insights of Muslim people on this topic. Can an Islamic person respect their religion and also live in a Western country and society which separates religion from laws and fully respect the laws of that country? So, for example, can a person follow Islam and also live according to American or European laws?

There are many Muslims living in the US. I have a very good Egyptian Muslim friend. He works, pays taxes, votes, citizen, has a 401k, a GA drivers license. He totally eschews Islamic terrorism, Sharia law, accepts Christian and Jewish friends, dresses like anyone else, kids go to local public schools. The only difference is that he prays 5 times a day and goes to the Mosque 2 times a week. He comes over for dinner and we say a prayer before meals. In our house we say Jesus, in his house he just uses God, not Allah. So, from a christian US perspective, I will say yes, commonly done.

Thank you. I have several muslim coworkers who are fully assimilated to US culture, but all describe themselves as "non-religious". I am still interested in responses from Muslim people who consider themselves to be "religious" as to whether they can abandon Sharia law and still be considered good, religious people such as by the people at their mosque and clerics, or if doing as your friend (and mine) have done puts them at odds with their faith community. I'm not looking to pass judgment, I just hear all kinds of opinions from American born people who are not Islamic people and would like to hear from someone who is a religious muslim.

Sharia law and being religious don't have to go together. Most religious Muslims don't subscribe to it any more than most Catholics abstain from sex except for procreation.
Sorry I'm putting in my 2 cents when I'm not Muslim.
I'm sure you can find religious Muslims who can give you their personal opinions, but maybe not more than 1 or 2 will see this question here.
I'd try some sites that are specifically Muslim and have Q and A.