When travelling through Dagestan by car, how far can risks of crime, harassment or political/cultural trouble be managed?

I think you know that it is not safe because you had to ask this question…

Your government (Germany I believe?) can provide you the explicit answer. Always check your national travel advisories!!

On their website, in regards to Northern Caucaus, the German government specifically states:

Traveling to the North Caucasus
Federal District and adjacent regions is an indication of the
increased security risk. In particular, not necessarily required trips
to Ingushetia, Chechnya and Dagestan is strongly discouraged. In the
above mentioned regions there is a higher security risk due to
attacks, armed conflicts and kidnapping cases than in other Russian
parts of the country. Persons who travel to the above-mentioned
regions despite the high risks can expect only limited assistance from
the German Embassy in Moscow in the event of an emergency. Short-term
restrictions on the right of travel for foreigners can not be ruled
out.

Border traffic with Georgia and Azerbaijan The Dariali / Hoher Lars
border crossing on the A 301 (“Georgian Military Route”), which
connects North Ossetia (Russia) with Georgia, as well as the border
crossing between Samur on the border between Dagestan (Russia) and
Azerbaijan are now back for the international Travel opened. However,
capacity-related difficulties in crossing the border can not be ruled
out. An entry via the Georgian-Russian border into the Georgian
conflict areas Abkhazia and South Ossetia will continue to be punished
by the Georgian authorities as an illegal border crossing.

Regarding the security situation in South Ossetia and Abkhazia, the
travel and security information of the Foreign Office for Georgia has
to be observed.

So, basically what they’re trying to tell you is, do not go there unless it is essential. It is up to you to decide what is essential and if its worth the risk. Keep in mind that the German consulate in Moscow is very, very far away when you’re sitting in a Dagestan jail or held for ransom. Just give it thought.

In regards to Georgia (and South Ossetia you asked about), as it is referenced by the Russian section above, the German government also specifically states:

Entry by land is possible via Turkey, Armenia, Azerbaijan and Russia.
Foreigners wishing to enter Russia from Georgia must use the Dariali /
Hoher Lars border crossing on the M3, the so-called “Georgian Army
Route”. Capacity-related difficulties at border crossing and resulting
waiting times can not be excluded. Above all, however, the security
situation in the North Caucasus should be taken into account: Travel
to Ingushetia, Chechnya, Dagestan, North Ossetia and
Kabardino-Balkaria is strongly discouraged (see Travel and Security
Policy Russian Federation ).

South Ossetia and Abkhazia Travel to Abkhazia and South Ossetia and
the immediate vicinity of the conflict region are strongly
discouraged. Consular protection can not currently be granted to
German nationals for lack of access. Even the feasibility of a rescue
flight to these areas is not ensured in an emergency.

Entry into Georgia – defected areas of Abkhazia and South Ossetia from
Russia continues to be prosecuted by Georgian authorities as illegal
border crossing, South Ossetia is closed to international travel, the
administrative border with South Ossetia is restricted area, since the
2008 war there is an increased danger from mines and unexploded
ammunition.

Due to the unpredictable security situation near the administrative
borders, it is strongly recommended that the area be avoided or that
Georgian authorities obtain prior approval. Abkhazia and South
Ossetia are not under the control of the Georgian government. Russian
troops are stationed in the areas and at their administrative borders.
The situation in the conflict regions is currently stable, but it can
change at any time. Therefore, inform yourself about the local media.

The Georgian “Occupied Territories Act” prohibits travel, economic
activity, land acquisition or real estate, as well as other activities
in Abkhazia and South Ossetia, with few exceptions. Infringements can
result in fines or imprisonment of up to five years.

Also on later trips to Georgia threatens the refusal of entry, it
should emerge from the pass that previously an illegal entry into
Abkhazia or South Ossetia / Georgia has taken place. Therefore, it is
strongly advised to be informed about the relevant regulations in a
timely manner, and to obtain the necessary approval from the Georgian
government. The Georgian Ministry of Foreign Affairs and the Minister
of State for Reconciliation and Civil Equality provide information and
permission to enter the country .

I recently visited Krasnodar, Sochi, Maykop, Stavropol and Tbilisi/Stepstanminda Georgia which is not too terribly far from these areas you are asking about. My Russian fiancee works for one of the large oil companies in Russia and they send her to Krasnodar region for work often, and its completely not safe at all for her. They must be off the streets at sunset and she must cover her blonde hair, to avoid trouble. I traveled through Georgia this past January, in the snow, and many trucks were lined up, unable to move. Keep this in mind, that the weather can greatly impact any travel to the Northern Caucasus mountains.

I also know my country (USA) specifically states that any travel is forbidden to Dagestan. USA state department outlines it here:

North Caucasus (including Chechnya and Mount Elbrus)

Civil unrest and terrorist attacks continue throughout the North
Caucasus region including in Chechnya, North Ossetia, Ingushetia,
Dagestan, Stavropol, Karachayevo-Cherkessiya, and Kabardino-Balkariya.
Local gangs have kidnapped U.S. citizens and other foreigners for
ransom. There have been credible reports of arrest, torture, and
extrajudicial killing of gay men in Chechnya allegedly conducted by
Chechen regional authorities.

Do not attempt to climb Mount Elbrus, as travelers must pass close to
volatile and insecure areas of the North Caucasus region.

The U.S. government is unable to provide emergency services to U.S.
citizens traveling in the North Caucasus region, including Mount
Elbrus, as U.S. government employees are prohibited from traveling to
the region.

Visit our website for Travel to High-Risk Areas.

Not safe at all. I don’t know what’s going on right now, but I remember seeing on news how local police cars were bombed, how someone drove a car to a police checkpoint and it exploded and how some random/police cars were shot near Mahachkala. Its usually local bands/rebels/boeviks from Dagestan/Chechnya and they usually target Russian police. However it doesn’t mean you can be 100% safe. There are many cases of abduction/ransom even nowadays. Just be careful.

This is challenging task, especially if you do not know the Russian. Moreover, it’d be considered as dangerous even for native Russians. North Caucasus is a place for unclaimed civil war for years, and each week something happen.

Here you may find unofficial news portal about current situation. In some cases the fact that you are tourist can help you, but in general it’s not a place you should take a drive. If you can, find a local guide so some situation could be resolved, but if I were you, I wouldn’t go there.

Even if you’re European looking people, it will be easy to understand that you’re not locals, as you probably do not have a beard, and your trip partner doesn’t wear appropriate (from local point of view) women clothes. It’s a high risk to became a victim of robbery, kidnapping or get a health damage.