That is an actual interesting point to consider.
Can you be a true Muslim believer and a fully pledged capitalist at the same time?
Up to what point the two ideologies converge or clash
On another point, that you mentioned
Only Allah knows who is a true believer. A Muslim can still be a true believer and commit crimes, he is a Muslim criminal. In Islam the deviant group that asks the same question you did and makes takfeer (excommunicates, making a Muslims blood permissible to spill) are known as the Khawaarij (ISIS/Daesh, Al-Qaeda, Taliban, Muslim Brotherhood etc)...
If a person believes in Allah (alone) as the only deity worthy of worship and believes that Muhammad is His Final Messenger to mankind and testifies to this, he is a true believer, whatever comes after this is between Allah and the Muslim (and consequently anyone the Muslim may have cheated or oppressed).
So yes, a person can be a true believer in Allah and His Messenger and still be engaged in corrupted activities ...that person can also repent and abstain from his crimes against himself and others and Allah may forgive him because Allah is the (Al-Ghafoor) Oft-Forgiving, Most Merciful (Ar-Raheem)...the same cannot be said about mankind tho, so...
Also, Allah will aide a person, Muslim or non-Muslim, so long as they are just and truthful, if they are opposite to this, Allah disgraces them, and the supplication of the oppressed, Muslim or non-Muslim, is answered by Allah, even if the oppressor is Muslim.
But for this to really make any sense, you have to know about Tawheed as was understood by the Companions of Allah's Messenger.