In other words, a synagogue identified with Conservative Judaism might be considered moderately liberal in its religious practices.
The distinction between “Reform” and “Conservative” makes more sense if understood in the context of the late 1800s and early 1900s when Orthodox Judaism was considered a backward and dying movement, and the question in the life of Jewish intellectuals was whether to make radical changes in Jewish religious life or to conserve a larger amount of Jewish practices in a modern context.
To the left, Reconstructionist Judaism is even more radical than Reform Judaism, and to the right, Orthodox Judaism can be divided into several different groups, of which the most relevant in an American context are the Modern Orthodox and the Hasidic groups, the latter of which is probably best known in America via the Chabad movement.
The revival of the role of Orthodox Judaism is a relatively recent phenomenon, one which is not unconnected with, on the one hand, the assimilation of less-observant Jews into mainstream Western society together with loss of their Jewish identity, and on the other hand, the higher birthrate and much higher commitment to Jewish identity among adherents of Orthodox Judaism.
We also need to recognize that unlike evangelical Protestants and traditional Roman Catholics where religious observance is a fairly good predictor of politically conservative views, that isn't necessarily true in Judaism. A significant number of politically conservative Jewish Republicans are nonobservant or largely secular in their religious outlook. On the other hand, for both historical reasons and factors of practical politics, strictly observant Orthodox Jews may vote for Democratic candidates, especially if they live in areas (New York City, for example) where a vote for a Republican is usually a wasted vote and the only vote that counts is in the Democratic primary.
All of this is only a quick summary and I'm not being fair to the movements described. Describing modern American Jewish practices requires a book, not a page.
I looked into a Conservative shul. At least in NYC they are nothing more than the retarded wing of the Reform movement, running about 10-20 years behind their heresies.
I’d probably add to your list, Modern Orthodox, which is pretty consistently Zionist and socially conservative.
I grew up the equivalent of Modern Orthodox (or, perhaps more correctly, non-Hasidic Orthodox) in Israel, but married into a Hasidic family.
Every USA citizen in our family is a TEA-Party side Republican.