If this chapter had to be reduced to a soundbite, it would be "Do not judge another." From that perspective, this lesson could not be more relevant in modern times. The context, however, of food and which church days are special, are not the primary issues generating judgement in present circles. Let's start with Paul's solution and then look at applications beyond the ones the early church was facing.
1. Believers are to act based on our reason and conscience. We are to use the measure of spiritual insight that we possess.
2. Believers are not to be quick to judge those who do not answer to us. God will give Insight concerning the edifying response if we ask.
3. The strong are not to place temptation in the way of the weak. Religious freedom maintains a link between insight and actions.
The book of Leviticus has an excellent framework for living. It points out that in life things can be classified as clean, unclean, or holy. Romans 14:23 echoes this sentiment by explaining that if we "act from faith" then matters of daily living will take care of themselves. This is a good overarching principal, but it can be tricky at times to apply to specifics. For proof, just read the rest of Leviticus where the attempt is made to assign every waking moment to the correct category.
In comparing the weak and strong Christians, Paul clearly puts the burden on the strong to nurture the weak. Just as in parenting, a balance must be struck between being too strict and allowing too much freedom. Discipline must be administered in love, not doled out in punishment. Paul Bunyon wrote that the tendency to dispute over opinions is the mark of a frivolous mind. It's easier to argue over details than to take on the real responsibility of discipleship.
In Paul's dealings with issues of food and worship, he encouraged mutual tolerance and respect, but tolerance here means more than non-judgmental inaction. It means offering loving instruction and being quick to deny ourselves the freedoms that we have through Christ. Insisting on our rights at the expense of another's conscience is the mark of a "stumbling block." For those who haven't fully understood the liberty that Christ offers, laws and traditions will still feel necessary. Paul's idea of tolerance for the strong is an acceptance of unnecessary limitations on themselves rather than an acceptance of destructive behaviors of the weak.
The Kingdom of God (14:17) is beyond trivial things like eating and drinking what we want and singing the songs we like in church. If we follow our convictions with integrity, and humble ourselves, then our hearts are more receptive to being led into the truth. We can serve God by observing rituals or ignoring them, but we do not have the option of denying the righteousness, peace and joy of the Spirit of God.