
It does seem somewhat inhuman to not want to help in some way, whether by donating money or volunteering your time. The question is what halakhah tells us to do with that natural reaction.
I. Darkhei Shalom
The simple answer is that there is an element of darkhei shalom, the ways of peace. We pray for all humanity in order to create a cohesive society in which everyone lives together in harmony. This might even make reciting Tehillim obligatory, although I highly doubt that we can obligate people to do so.
Click here to read moreHowever, on a small scale, in any given shtiebel, darkhei shalom might not apply. What is the case then?
II. Bentching in a Gentile House
The Magen Avraham (189:1) writes that when bentching in the house of a Gentile, you should change a phrase towards the end to "ken yevarekh osanu kulanu yachad bnei bris -- may He bless all of us together, people of the covenant." That addition of "bnei bris" is to exclude the Gentile because the prohibition of lo sechanem, of giving a gift to a Gentile, prevents us from blessing him (except when darkhei shalom applies).
The Magen Avraham quotes a Taz (Yoreh De'ah 232:14) who agrees in principle but thinks the language needs to be more explicit. The Ba'er Heitev (189:1) and Sha'arei Teshuvah (189:1) quote this rule without dissent.
This would imply that it is prohibited to recite Tehillim for Gentiles because of the prohibition of lo sechanem. It noteworthy that neither the Mishnah Berurah nor Arukh Ha-Shulchan quote this rule, nor have I seen it in any siddur or bentcher. Although this could be due to fear of Gentile authorities. The contemporary Piskei Teshuvos (vol. 2 189:4) does, however, quote this rule.
III. Gentiles Today
The assumption underlying this approach is that Gentiles today fall under the prohibition of lo sechanem. However, it is common within Modern Orthodox circles to assume that this is not the case. Many adopt the view of the Meiri, that the prohibition only applies to Gentiles who are unlawed and uncivilized. Non-Jews today are civilized and lawful; therefore, none of these rules were intended to refer to them.

According to the Meiri, R. Soloveichik and others who agree, there is no prohibition against reciting Tehillim for Gentiles today because lo sechanem does not apply to them.
After Ma'ariv tonight we recited Tehillim. Then, as we naturally segued into "Achenu kol beis Yisrael -- Our brothers, all the people of Israel" that is usually said after Tehillim, I was unsure whether it was appropriate or some other more universal phrasing should be substituted. Then someone told me that there are Jews in Haiti also, which resolves the wording question and pretty much renders all of the above academic. Nevertheless, R. Soloveichik and others provide a powerful message for today's crisis.