In our day and age, feelings seem to win out in virtually every area of life. While some people would consider this to be progress, I do not believe this is best for society-at-large. Feelings are important in the micro (i.e. interpersonal realm), while values are important in the macro (i.e. larger society). Unfortunately, many people do not make this distinction.
This can be easily traced to the ongoing conflict between the Palestinians and Israel. As long as the majority of media outlets show images of "poor" Palestinians throwing rocks against "wealthy" Israeli tanks, the average uneducated viewer (I'm leaving out blatantly anti-Semitic viewers, who will be against Israel no matter what) will feel for the Palestinian. What is clearly missed in all this is any value of right and wrong. It doesn't take a rocket scientist to figure out that Israel is simply defending its citizens, and that the reason many Palestinians live in meager neighborhoods is because of the corruption and depravity of their leaders (a.k.a. terrorists). They spend their time thinking of ways to destroy Israel rather than to build homes, hospitals and schools on land their enemies left.
Just think of the last time someone asked how you feel about a particular issue. Unless they're wondering if you have a fever, they should really be asking what you think about that issue. Without taking this idea too far, all I'm trying to point out is that we have allowed emotion to replace thought in many areas of life. And we have paid a dear price for it. For example, instead of focusing on the substance of a particular topic, many people will have an emotional outburst when someone disagrees with them - and it's often respected as a valid response! This ruins any chance of having an intellectual discussion about politics, religion or any other area of life. Unless it's an existential issue, we shouldn't take differences of opinion personally.
By the same token, there are interpersonal cases where more compassion should be exercised. For example, Rabbi David Levin (grandson of Rabbi Aryeh Levin, one of the most righteous Jews in history) served as a chaplain in the Israeli Air Force. While caring for a bereaved military family, he saw them playing live music at the grave site of their loved one. This made him very uncomfortable because it is not permitted according to halachah (Jewish law). However, Rabbi Levin used good judgment and was able to discern that, although he disagreed in principle, it would have been a worse offense to say something harsh or demeaning to the mourners. Perhaps one day that family will become more connected with their Jewish roots because of Rabbi Levin's kindness and tolerance.
Feelings and values both have their place, but we have to use our seichel (common sense) to determine when one overrides the other. In cases of upholding standards of objective good and evil, values must win out; otherwise (to paraphrase Pirkei Avot 3:2), people would eat each other alive. However, in cases of upholding interpersonal decency, feelings are there for a reason; otherwise, we would constantly be bickering over every slight detail that others didn't perform precisely as we saw fit. While it's crucial to have both strong values and compassion for others, it's just as important to know which one to implement in a given situation.