This is a complicated question: Many people have stated that it is the obligation of Jews in the diaspora to counter "bad PR" about Israel. The difficulty comes in when we consider what that "bad PR" is: a great deal of it is not "public relations" at all, but genuinely bad things that happen in Israel due to political decisions of the Israeli government, or sometimes crimes and violence committed by certain groups of Israelis for political reasons.
Since the great majority of the "bad news" has a factual basis, from a religious point of view there are two conflicting values: the first is that there is a principle based in the talmud that it is forbidden for one Jew to inform on another. Strictly speaking, the prohibition is to inform on individual Jews to a non-Jewish government, and there are exceptions to this rule even early on, such as that one who engages in conduct that endangers the community maybe informed on. In addition, there is some disagreement by modern commentators about how this applies in countries with a secular government which is not inherently oppressive of Jews.
There is a (for this matter, anyhow) somewhat related principle that one shouldn't commit a chillul haShem: in other words, one shouldn't cause others to think badly of the Jewish God. In terms of our current question, this principle has bent both ways. In one mindset, the idea has become that one should never say anything bad about one's fellow Jews, because it will cause others to think poorly of Judaism. However, the principle can also be faced the other direction; we'll see how in a bit.
Together, the two concepts have morphed from Jewish legal guidelines to a sort of folk idea of not creating a "shanda fer di goyim" -creating a shameful view of Jews to non-Jews.
However, a second concept that must be taken into account is that of the obligation to rebuke. The Torah (Lev. 19:17) commands us, " You shall not hate your brother in your heart: you shall surely rebuke your neighbor, and not bear sin because of him."
In the talmud, there is a wonderful passage explaining this verse which states: "Whoever can prevent their household from committing a sin but does not, is responsible for the sins of their household; whoever can prevent the people of their city, is responsible for the sins of their city; if the whole world, one is responsible for the sins of the whole world."
If Israel is doing bad things, then we are obligated to try to stop them.
Finally, there is a further consideration about what it means to speak publicly in the modern world. Not so long ago, it was possible to keep information under wraps, more or less. Today, that is simply impossible. Technology and social media have made information freely available. The idea that, somehow, failing to speak about bad things that are happening will keep people from knowing about them is hopelessly naive. The average high school student has constant access to all sorts of information, 24 hours a day. Moreover, simply trying to counter serious problems by talking about good things to "balance" them is absurd. Does a new iPhone app counterbalance spitting on an 8-year-old?
To solve problems we must necessarily make it clear that we are aware of these actions and object to them. At the same time, we shouldn't forget the first part of the verse in Leviticus, "You shall not hate your brother in your heart." Criticism must come from a place of love: we don't criticise to destroy, but to repair. However much it hurts, speaking out about extremism and violence is a necessary part of our relationship with Israel.
Trying to hide what's going on, either by not talking about it or by "countering" it with good news is more likely to be counterproductive than helpful. People already know what is going on. If we love Israel, then we are obligated to try and make sure that we do not hide the problems, but to the contrary, are very open that 1. we are working to try to fix these very real problems and do not regard them as things that we simply need to put a different spin on, and 2. that at the same time, we love Israel and care about Israel's people, who are our family.
By doing both of these things, we make it clear that Jews and Judaism are not monolithic; that we understand that there are problems that cannot be left to fester; that we also believe that these problems can be solved; that we believe that these problems should be solved peacefully and politically; that we are willing to put pressure on Israel to make the Israeli government act to address the problems, and that we fully support the continued existence of the state of Israel and that solving these problems is part of ensuring Israel's safety.
It's fine to talk about good developments that are coming out of Israel, and when it's appropriate we certainly should talk about them. At at the same time, we are doing no favors to Israel if we pretend that everything will be fine if nothing changes. Is it painful to have to admit that there is a geat deal that needs to be fixed in israel? Yes, it is. So I finish with a quote from the chasidic rabbi, Menachem Mendel of Kotsk: "The one who increases knowledge, increases pain (Kohelet 1:18). And what does this mean? It is worth it for a person to increase pain, provided that they increase knowledge as well."
Answered by: Rabbi Alana Suskin