Torah should matter in the concrete, daily lives of Jews, and therefore Torah must speak to political issues. Budgeting priorities, health care access and quality, legitimate grounds and tactics of war – these are precisely the types of issues that Judaism in particular cares deeply and has much to say about.
This remains true even when those issues become the subjects of partisan debate. If Democratic policies will fund the abortion of many late-term fetuses that would otherwise be born, and a rabbi sees late-term abortion as murder, how can s/he not say so? If Republican policies will deprive many people of their basic human dignity, how can a rabbi not say so?
It is true that political parties take positions on many, many issues, and individual politicians do not agree with all the positions of their party, so a religious claim that one must vote a particular way is always oversimplified. I think it is almost always wiser to discuss and weight the values involved and let listeners reach their own conclusions. But the job of a religious leader is to set priorities in complex circumstances.
It is also true that voting involves a judgment of consequences, not just of intent, and rabbis often have no particular qualifications to judge consequences. But neither do politicians, and in any case, all legal and moral decisions require judgments as to facts and consequences. We should train religious leaders to be expert in these areas, as much as or more as we train them to be expert at dealing with the emotional consequences of personal decisions. (Of course, rabbis, like everyone else, should avoid speaking out of ignorance, or lecturing the more informed.)
Nonetheless, pulpit discussions of partisan issues are often unwise, and even unfair if an expectation has been set otherwise. The Jewish religious community generally aggregates along ritual rather than ethical/political lines, and therefore it is practically necessary for rabbis to get along with members of both parties. Rabbis who talk primarily about politics, and in partisan fashion, will reasonably be suspected of imposing their ideologies on Torah rather than deriving them from Torah.
This does not mean that ritual is more important, or naturally a more appropriate topic for rabbis, than politics. Decisions to aggregate along ritual rather than theological grounds, or on ritual rather than Zionist grounds, do not require us to consider nusach hatefillah more important than the national existence of the Jewish people, or precise kashrut standards more important than precise standards of monotheism – they simply reflect practical judgments as to the best way of advancing our collective interests. I suspect that much American Jewish rhetoric on the subject of religion and politics is a product of IRS regulations and of our status as a minority religion.
Bottom line: Rabbis cannot, and congregants should not, see political issues as offlimits. Rabbis are wise to make such pronouncements sparingly, and with humility – they should make clear that even their wisest, most Torah-grounded judgments do not exclusively or unquestionably represent G-d’s true will. But they are entitled, and sometimes obligated, to vigorously seek to persuade their congregants to act in accordance with their best judgment as to G-d's true will, even when His will does not command a political consensus
Yes, a rabbi can discuss partisan political issues BUT it depends how he or she does it. A rabbi will be more successful in discussing partisan issues when he or she lays out the arguments on both sides of the issue. This way both sides feel heard, even if the rabbis decides to offer her or his view on which side she or he supports. A rabbi should try to be as inclusive as possible so that everyone in the community feels like they have a place there. Respectful honest debate on issues certainly has a place in a Jewish setting. After all this is exactly what the rabbis of the Talmud did. They debated everything. Tone, safe space, and open conversation are key to a successful conversation.
This is a very personal question that truly depends on the Rabbi and his or her relationship and covenant with the congregation.
There are Rabbis that strongly believe their role as leaders requires them to address burning issues even if these are partisan political issues. As long as they ground their approach in a Jewish teaching rater than a personal agenda, this is definitely a legitimate thing to do. They follow in the footsteps of great Rabbis that were never afraid to express an opinion even when that opinion could be controversial.
Other rabbis believe that politics altogether should not be brought into the spiritual experience of a Shabbat service and that addressing such issues should take place in special designated program where participants chose to come and listen rather then being a "captive" audience at a Shabbat service.
Both approaches are legitimate and should be adopted through mutual understanding between the rabbi and congregation