Perhaps the most concise way to answer this is to share influential commentaries from Doctors of the Church and others whom the Catholic Church draws from. (All bolded text is from me).
St. John Chrysostom — "Here he seems to me to be giving a gentle hint about fasting"
This Doctor of the Church contends that Paul is speaking about fasting, condemning those who fast on some fixed days but not others. Although Paul is more strong in his critique in other books, he suggests that the faith of the Romans was newly developed, and thus he was more gentle in his correction.
Here he seems to me to be giving a gentle hint about fasting. For it is not unlikely that some who fasted were always judging those who did not, or among the observances it is likely that there were some that on fixed days abstained, and on fixed days did not. Whence also he says, Let every man be fully persuaded in his own mind. And in this way he released those who kept the observances from fear, by saying that the thing was indifferent, and he removed also the quarrelsomeness of those who attacked them, by showing that it was no very desirable (or urgent, περισπούδαστον) task to be always making a trouble about these things. Yet it was not a very desirable task, not in its own nature, but on account of the time chosen, and because they were novices in the faith. For when he is writing to the Colossians, it is with great earnestness that he forbids it, saying, Beware lest any man spoil you through philosophy and vain deceit, after the traditions of men, after the elements of the world, and not after Christ. Colossians 2:8, see p. 4 And again, Let no man judge you in meat or in drink Colossians 2:16, and, let no man beguile you of your reward. Colossians 2:18 And when writing to the Galatians with great precision, he exacts of them Christian spirit and perfectness in this matter. But here he does not use this vehemency, because the faith was lately planted in them. Let us therefore not apply the phrase, Let every man be persuaded in his own mind, to all subjects. For when he is speaking of doctrines, hear what he says, If any one preaches unto you any gospel other than that you have received, let him be accursed , even if it be an angel. And again, I fear lest by any means as the serpent beguiled Eve through his subtlety, so your minds should be corrupted. 2 Corinthians 11:3 And in writing to the Philippians, he says, Beware of dogs, beware of evil workers, beware of the concision. Philippians 3:2 But with the Romans, since it was not yet the proper time for setting things of this sort right, Let every man, he says, be fully persuaded in his own mind. For he had been speaking of fasting. It was to clear away the vanity of the others and to release these from fear then, that he said as follows: [the commentary continues with verse 6]
St. Augustine of Hippo — "It it is not about two men here, but of man and of God"
The "Doctor of Grace" suggests that the passage can be read as metaphorical between man who judges differently on different days and God who judges the same every day (although he admits that there are likely more accurate translations).
(Romans 14:5-6) “One, for example, judges on alternate days, another, on the other hand, judges any day.” Leaving aside, for the moment, some possible more accurate consideration, I believe that it is not about two men here, but of man and of God. He who makes judgments every other day is man, because he can judge today one way and tomorrow another; can today condemn one as bad, convicted or confessed, and tomorrow it turns out that it looks good, since it has been corrected. Or the other way around, today he praises one as a good person, and tomorrow he seems a degenerate. But he who judges every day is God, because he knows not only how each one is now, but how he will be day after day. Then: “Everyone is sure of their way of thinking,” says Paul. That is to say, each one arrives in his judgments to where it is allowed to the human understanding, or to each man in particular. The one who thinks one day, he continues, does it for the Lord, that is, what he judges correctly today, he does for the Lord. The one who gives exact judgment only for one day, regarding someone whose fault you see today as evident, is for you to learn that there is never to despair of its correction.
George Leo Haydock - "It is without grounds that some would pretend from hence, that Christians cannot be bound to fast, or abstain from flesh on certain days"
Although not a Doctor of the Church, his commentaries on the Douay-Rheims Bible are enduring. Haydock interprets this passage as focusing on the differences in opinions between those who wanted to keep the Mosaic law regarding days of fasting and those who did not. However, he makes it very clear that this difference does not apply to modern Christians, and that the Catholic Church could still institute these. In other words, Paul's instructions should be narrowly focused on the particular issue at hand.
Between day, &c. Still observing the sabbaths and festivals of the law. Ch.—And another judgeth every day. That is, thinks every day to be taken away, that was to be kept, merely because ordered under the Jewish law. And now since both they who keep days, or do not keep them; and they who eat or who abstain, do these things with a regard to God, and according to their conscience, let no one judge, or condemn the one party, nor the other; in these things, let every man abound in his own sense. It is without grounds that some would pretend from hence, that Christians cannot be bound to fast, or abstain from flesh on certain days. The apostle speaks only of the distinction of meats, called clean and unclean, and of fasts or feasts peculiar to the law of Moses. It does not follow from hence, that the Catholic Church hath not power to command days of fasting, and abstaining, for self-denial or humiliation. Wi.—The apostle here treats only of the subject in hand, viz. the Mosaic distinctions of clean and unclean meats: and in this he allows, for that present time, each one to follow his own private judgment.** S. Chrysostom observes that S. Paul did not wish the weak to be left to their own judgment in this, as in a point of no consequence; but that they should wait for a time. The converts were not immediately prohibited their accustomed practices, but they were tolerated in them for a while, till fully instructed. This we see in many of the converts at Jerusalem, who were still observers of the Mosaic ordinaces; this was tolerated, that the synagogue might be buried with honour. Estius.
