Orthodox/Conservative/Reform are "denominations" of Judaism; "sect" isn't quite the right term. ("Sects" tend to vote in a bloc; good luck getting all Orthodox Jews to agree on anything politically.)
Unless otherwise specified, you'll hear an Orthodox perspective here. The following answer reflects Orthodox Judaism.
The Talmud takes for granted that there was a spoken law accompanying the written one; often what was written to sound as a very harsh punishment was actually intended under extremely limited conditions. (Similarly, "an eye for an eye" meant that was what was deserved, but the courts actually just demanded financial restitution.) Talmud said the death penalty was incredibly rare; when murder rates shot up, the unsolved-murder ritual stopped being used as the sight of a murdered body no longer shocked anyone; similarly when the general state of marriage in society fell apart, they stopped doing the suspected-adulteress ritual as it no longer shocked anyone. So the prescribed death penalties were only used when the crime was rare and shocking. And the perpetrator warned, and s/he verbally acknowledged the warning, and ...
(The Talmud further adds so many caveats and provisos to the rebellious-son law that at least in one opinion, it was never actually carried out. Rather it's there for the moral teachings behind it.)
Furthermore any application of the death penalty requires Jewish self-rule (the Jews told Jerome that's why the Book of Susannah wasn't canonized).
Furthermore, corporal punishment requires a panel of rabbis who have "super-ordination", which was ended by the Romans c. 600 CE. (There have been some interesting attempts to reboot such ordination ... but that's another conversation.)
Thus: anything that Leviticus says deserves death is still deemed "a very great sin", and if someone is stuck in a situation choosing the lesser of two evils, then a sin that never warranted the death penalty is less-bad than one that theoretically could. But to actually carry out such penalties required very rare circumstances that are entirely impractical today.
There's a letter from Rabbi Moshe Feinstein, the most prominent American Orthodox authority on halacha for a good part of the late 20th Century, to Governor Carey of New York, as the latter (a Catholic) was considering ending New York's death penalty. Rabbi Feinstein was not pushing for or against New York's penalty, simply defending Judaism's past use of capital punishment as being very rare and having appropriate safeguards.
As your question stated "halacha" in general (no definite article required, just as you wouldn't say "the canon law") -- Jewish civil law is alive and well. If two Jews in Omaha have a contract dispute, they are supposed to go to a rabbinic panel and have it settled according to halacha, rather than duke it out in Nebraska state court. (Of course as far as the State of Nebraska is concerned, if two parties in a civil suit want to settle out-of-court, or go for arbitration/mediation, go for it! So the parties will ideally sign a legally-binding arbitration agreement agreeing to follow the ruling of the rabbinic panel.)
On the other hand if you live in Omaha and someone breaks into your house and shoots at you, that's not a job for the rabbis! That's a job for local law enforcement and the criminal-justice system.
In Israel, parties in civil cases have the option of going before a rabbinic panel following Halacha, or instead using "secular" Israeli law -- itself largely derived from the colonial empires (Britain and the Ottomans) previously ruling there. Israel's first chief rabbi, Isaac Herzog, wanted to see more of Halacha implemented in civil law, and to this day there is a school of thought trying to incorporate more Mishpat Ivri -- "Hebraic Code" in civil suits. As people have their choice on this (and a large portion of the Israeli public has no interest in the rabbis), the status quo seems to work pretty well on this.
Lastly we get to family law. For instance, the Talmud says there is simply no way a marriage can be effected halachically between a Jew and a non-Jew. Ergo virtually no Orthodox rabbi will perform an intermarriage (barring some very, very interesting mental gymnastics). The US, of course, lets people get married by a justice of the peace irrespective of their faiths (or lack thereof). You don't hear American rabbis trying to change US law on that; history has shown that once you single out Jews for special treatment in the law, it doesn't end well.
The Ottoman Empire left family law up to each community's faith group; this became British policy, and then shifted smoothly to the Israeli policy. This means anyone who wants to get married or divorced in Israel has to go to officially-recognized clergy for their faith. (Or they can get a civil marriage/divorce in another country, which will then be recognized by the "secular" legal authorities upon their return to Israel.) A Jew-and-non-Jew couple, or for that matter a kohen and a divorcee, will be turned down by the Israeli rabbinate even if the couple doesn't care a fig about halacha. There has thus been a push for Israel to allow civil marriages. (To be fair: there are other reasons at play here.) I'd imagine most Orthodox rabbis prefer the status quo as it does prevent many problems, but there are some who feel that the mixing of political power with religious influence is toxic and that Israeli law should be more liberal on this too. (Not that they would marry a kohen and a divorcee, but that religion is best spent convincing than forcing.)
