I think you're getting confused over word choice here...

Looking at the context of the verse, it seems that perhaps "prejudice" is more fitting than "favoritism". The example is that of showing preference to the rich man as opposed to the poor man - without knowing anything more about each man other than their outward appearance.

Let's look at other translations:
[NASB] - 1My brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism.
[AMP] - 1MY BRETHREN, pay no servile regard to people [show no prejudice, no partiality]. Do not [attempt to] hold and practice the faith of our Lord Jesus Christ [the Lord] of glory [together with snobbery]!

Merriam-Webster defines it as:
FAVORITISM 1 : the showing of special favor : PARTIALITY
PARTIALITY 1 : the quality or state of being partial : BIAS
BIAS 3 a : BENT, TENDENCY b : an inclination of temperament or outlook; especially : a personal and sometimes unreasoned judgment : PREJUDICE c : an instance of such prejudice
PREJUDICE 2 a (1) : preconceived judgment or opinion (2) : an adverse opinion or leaning formed without just grounds or before sufficient knowledge b : an instance of such judgment or opinion c : an irrational attitude of hostility directed against an individual, a group, a race, or their supposed characteristics

So you can see it's not really about showing favor towards one friend vs. another, or having a favorite brand of cereal, or favorite type of food - the problem is showing undue or undeserved favor, or prejudice towards people.

The key word is "undue", in this case - imagine you were a judge presiding over the trial of two men. Both men have committed the same exact crime - one is Caucasian, the other is Indian. Favoritism in this case would be you giving the Indian a lighter sentence because you are Indian yourself and like Indians, and all that they stand for, such as curry and vindaloo. That's a pretty blatant example. However, don't confuse the reasoning with the outcome. If you were to give the Indian a lighter sentence because he didn't have a criminal history whereas the other man did, then it would be perfectly valid and reasonable.

God definitely shows favor towards certain peoples - Abel over Cain, Isaac over Ishmael, Jacob over Esau, Jews over Gentiles - but I don't think it was ever prejudiced. When Jesus chose the apostles, he did so on their merits, on what he knew they would do for him, what they could accomplish. He didn't choose them simply because they were rich and not poor, educated and not simple, eloquent and not stuttering - he chose them for who they were and what they would do for him. That's not prejudiced or favoritism at all.

As an aside, when you come across a difficult word or passage, it's really helpful to look at the word choices used by other translations, look up the definition of the words in a dictionary, and go to the original Greek/Hebrew word meanings - trust me, it'll save you a lot of time and stress in the long run :)