It is worst with Offroad but also happens with other non-armored wheeled vehicles (Boxer Truck, Quad bike, ...)

I am quite sure this is the type of bush (the small one on the dirt road) http://www.tacticalsites.com/~arma/Graphics/articles/TanoaPhotoReal_Large.jpg

+1000
The discussion about a problem was at a forum.
https://forums.bistudio.com/topic/189687-wrought-iron-bushes/
Occurs on all cards. It seems depends on settings of the server. I can be mistaken, but dependence on the parameter of level of armor (protection) of vehicles seems to eat.
It is possible as that to divide these dependences, or to make bushes and small fences out of a risk zone for transport and players? Strongly irritates when you lose health and wheels on these objects.
On speed of 30-40 km\h it is possible to turn over by car.
Fences have color of texture which it is badly visible against the background of a landscape, even when you don't move.
http://stroybat.ucoz.ru/raznoe/Error/2013-11-08_00001.jpg
In the editor it isn't reproduced. But it works at servers, somehow bushes and fences gain rigidity to damage from cars.
The problem has appeared not yesterday, it was from the very beginning.
Everyone thought that it is known to you, waited that it will be corrected.

Are you able to reproduce the bug in SP?

Also, if this happens only in MP, does it happen on vanilla game, without any special server settings (something that would change the vanilla settings but is accessible for example in difficulty - like for example reduced damage). If this is however caused by some custom server or game settings, I am afraid there is not much we can do about this (unless its on Official BIS Server).

True!!! Tested vanilla, it is caused by wasteland mod! :) Thanks for asking, can be closed!

There is no MOD.
When I start a mission at myself on PC, this problem is absent.
There are no settings of damage in Missie.
Tell what parameter (where this parameter) in a game on the server influence rigidity of bushes and fences?
What forces the car to fly up on bushes as on a springboard, to break wheels, to sustain injuries.
https://youtu.be/Ab44ulXO9_s

No parameter changes "rigidity of bushes and fences" however in difficulty settings, there is an option for increasing or reducing damage. However reducing damage would seem to do the opposite.

And while the Wasteland is not a MOD, vehicles there might actually be altered in some way by the mission scripts (that would be rather question for the mission author however). So far I was able to see video of the issue from the Wasteland mod? Are you able to reproduce the issue in some showcase or a editor mission?

If we talk about the damage, where and in what form the players should receive it? I understand there is a system of obtaining damages. But why the system applies to the whole environment? It looks in the game more than absurd.
Damage as such must exist?
I can not reproduce the problem on your PC in this mission. That is, there is no problem in the mission itself.
The game is also no problem.
How does the server creates a problem. This is not one or two servers.
I went to the official server (mission "End Games"), there is not so much damage from the bushes and fences.
Settings damage anywhere, but it's there.
To explain this phenomenon, the mission developer, too, can not.
The developer of the mission said that does not find a solution to this problem.

Sorry I am having hard time understanding what you are trying to explain.

Getting a damage from environment is pretty normal, as in normal life, when hitting an obstacle, you might damage your car. Though of course driving through a small bush should be alright, however, SP seems fine and as you said End Game (MP) also behaves as expected so this seems to be a Wasteland-specific issue so far so there is not much I could start with.

The developer of a mission and the administrator of the server don't know how to resolve an issue with damage of the equipment from bushes.
Arma3 developers don't know how bushes receive properties not peculiar to bushes.
Control of a mission has no parameter - the level of damage of cars.
The mission (video of demonstration of a problem from a mission) doesn't reproduce a problem on a host server.
The mission reproduces a problem on the dedicated server.
Who can explain emergence of a problem on the dedicated server?

Servers where this problem is present:
http://www.gametracker.com/server_info/arma3.noip.me:2402/
http://www.gametracker.com/server_info/arma3.noip.me:2402/

The mission:
https://www.dropbox.com/s/wvl8x0a8edhays9/becti_0097_z1321A3.Altis.zip?dl=0

So only on dedicated server, not on direct. Will look into that some more but so far no luck :(

Nobody knows in BIS what parameter in the "client settings" setup of the server causes damages from bushes?

Perhaps, it is control of complexity of a mission on the server. For example, configures setting - resistance of buildings to damage. I don't know what parameter is responsible for it. This parameter can, influence resistance to damage, fences and bushes?
What I have found on feedback with this old question.
https://feedback.bistudio.com/T63264