Can these vortices be dangerous?
While @Peter Kämpf 's answer is great and sufficient to answer the question, I would like to add a clarification (which should be a posted as a comment, but is too long for this format).

In the image in the question, there are visible streams of condensed water vapor from the atmosphere. These streams are only present at the blade tips. The question seems to assume that these streams depict the wake from the propellers. They don't, or more accurately there are only a very small part of the wake volume.



1. Images of tip vortices from different devices

1a, tip vortex from a propeller


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Condensed water forms because the change of pressure is adiabatic, in simple terms it occurs with little exchange of heat with the neighboring regions. It occurs first where the pressure difference is large and the transition quick. (By the way, note the 8 rockets used to assist for takeoff.)

1b, tip vortex from a wing


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1c: tip vortex from a rotor


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There is not doubt the rotors spin in opposite direction.

1d, tip vortex from a wind turbine


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Notice: Actually after looking at oddities on this image (the direction of the wind), I realized that this is an experimental turbine used by the US DoE and the NREL to study winds. The white stream is actually smoke released from the blade. Probes are visible on the leading edge to measure speed at different locations of the blade. I keep the image as it's a good one.



2. Full wake turbulence

Contrary to the previous images, the ones below show the whole turbulence created by the same airfoils. While the tip vortices are materialized by condensed water vapor created by a transition from high to low pressure at the tip of the devices, the whole wake is visible only if air is not clear.

2a, turbulence from a propeller


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Principle (no photo found, do you have one?)

2b, turbulence from a wing


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2c: turbulence from a rotor


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2d, turbulence from a wind turbine


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3. Images where both effects are combined

Note that regardless of whether they are visible or not, both the tip vortices and full wake always exist. Their visibility greatly depends, like contrails, on the air moisture and temperature.

As explained by @Peter, the energy of the tip vortices is diluted in the energy of the actual wake turbulence:


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Source: What causes a plane's wing tips to leave a small white vapor trail?



4. Complexity of the wake

Wake from a wind turbine, mixing all sources of turbulence:


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The tip vortex is initially a very small part of the wake, created by the high pressure air escaping from the low side of the wing. The whole wake volume grows in length and diameter as the airfoil moves. The vertex diameter grows, until there is no more energy left and air stops moving (see images in §3):


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See this question for details: How does an aircraft form wake turbulence?