Yes there are hazards, and you do want a captain who understands them and takes precautions. However anybody with an Airline Transport Licence would be expected to know about them, and the airline itself will have specific internal policies for operation into and out of jet streams.
The main hazard of jets is they are a major source of Clear Air Turbulence. Jets associated with fronts form in the warm air corner, on the warm side of the frontal boundary and under the tropopause. CAT occurs in the shear zone along the edge of the jet, typically on top of the jet at the tropopause or along the frontal boundary adjacent to the jet. There are other types of CAT, which occurs with sudden changes in wind velocity not associated with convective cloud, such as under the crests of mountain waves where rotors can form.
Jet streams may be indicated as a probability in weather charts, by pilot reports, or you may just find yourself entering a jet by the sudden ground speed change or heading change (if you're flying across it).
Lenticular clouds are another warning sign of CAT, the clouds indicating the mountain wave top, which means you can expect CAT blow the lenticular cloud.
In any case, if CAT is expected, you normally will slow down to Turbulent Air Penetration speed, and make sure everyone is strapped in. If CAT is really severe, and you are going too fast, people who aren't strapped down can get hurt, and there is an outside chance of damaging the airplane.
So basically the jet stream itself is not a problem, but the turbulence associated with shear zones at the boundaries is. And if you blundered into a jet that was a headwind you hadn't planned on, you might need to shift your route to get out of it.
To be clear about the concerns of DEI in the industry, it's not about resistance to minorities and women in the flight deck. It's a concern about standards being reduced to meet arbitrary DEI targets, because such targets, if enforced unreasonably by management under the gun to do-or-die due to political pressure, introduce a basic math problem; that is, the quota target necessarily reduces the talent pool, and if a directive from on-high says meet the target or else, reductions in standards may be the only option to meet the quota. That's the key concern.
If the US, the Colgan Rule, that requires 1500 hours to fly transport aircraft in airline operations, had a similar perverse math effect, by reducing the talent pool by excluding top notch copilot candidates just because they had less than 1500 hours (many of whom were likely female and minority). Regional operators were bitterly opposed to this because it put them in the position where they were forced to discard a superstar candidate's resume with, say, 1300 hrs, in favour of midwit candidate's with 1700. Such an arbitrary limit had little safety value in reality.