Jesus said, "No man can serve two masters, for either he will hate the one and love the other, or he will hold to one and despise the other." (Matt. 6:24)
A modern reading of that might suggest that someone cannot hold two jobs without some inner conflict. That is simply not true - but what Jesus said is true. The difference is in what the word "serve" means.
Jesus was not talking about a job, or serving as we generally think of it in terms of modern work. Jesus was speaking about the dedication of your life. The key is in the term "master".
In that day, serving a master was the meaning of one's life. It meant slavery, or something very much like slavery. The service of one's master was the meaning and substance of their lives and daily existence. How and when, and even whether or not you ate, or slept, or where you would stand, or what you would do with your time was determined by the master and your service. There was no time 'off' in these master / servant relationships. There was no 'free' time, necessarily. The servant lived for the service of the master.
That is why they could not serve two masters. It would mean that the meaning of life and the rationale behind each action and decision would be divided by the 'service' of two masters, and those needs, demands, and duties would often be in conflict, and sometimes be utterly contradictory.
In such a situation, you simply would have to choose - do I help my master 'A' or do I serve the interests of my master 'B'? You would either hate the first one or love the other - by your actions and decisions - or you would hold to the first master, and despise the other by not serving him.
This principle also applies to us.
Either you are with Christ, or against Him. Jesus actually said that once, in Matthew 12:30. There is no neutral territory, and there is no 'splitting the vote.' Your heart, mind and life are with Christ, and you serve Him in the same sense as the ancient "servant" in the time of Jesus, or your real allegiance is with someone or something else.
Either you are a Christian, or you are not. Jesus said it is either one or the other and if you try to juggle both you are doomed to fail and even the attempt is completely rejected by God. Either you love God, trust God, and serve the one true God, or your "god" is someone or something other.
Jesus was always a very black and white kind of guy - there aren't any "grey areas" when it comes to Him, and He proclaims the truth of God as He speaks - in part, because He is God.
Jesus drops the hammer, so to speak when He said that "You cannot serve both God and mammon." Now "mammon" is an Aramaic word which literally means "confidence", but it was used to refer to riches, or one's confidence in riches.
Mammon, for us, refers to "stuff," the things of this world and of this life. Jesus is referring to a devotion to such things - He mentions clothing, food, and drink. His list was not exhaustive, but more in the way of examples, the most common and powerful distractions - or types of mammon. Jesus chose the universal and most frequent focus of human concern to make His point.
His point is that to focus first and foremost on "stuff" is idolatry. It is unbelief toward God and a form of worship, or "service", toward the mammon of choice.
By the term, "unbelief", I do not mean that you doubt God's existence, or any specific doctrine about God. I mean a lack of trust, because that is what Jesus was talking about. He draws our attention to the birds, and tells us to notice how God supplies their need.
Jesus says, we are of greater value to God and He will take care of us.