I don't see that it is dangerous at all.
Being someone who lives life according believing in the round earth theory, I don't see any harm in a community of people trying to prove otherwise.
It doesn't really affect anything in my life, or their own, members of their family etc. if they believe the Earth is flat (for the sake of this point, I am not saying that it is or is not flat), just like it doesn't really affect them if I believe the Earth is round.
When this does become a problem is when you get idiots who seem to think it is right to abuse others, either physically or mentally, because their view of something that is relatively trivial, differs from their own.
(I firmly believe that the stuff I have said above should also adhere to religion, country of birth, colour of skin, age, etc.)
As another user has put, there have been "studies" into other topics, like vaccinations, that were completely untrue but pushed nonetheless. Believing in these is dangerous as these can actually have an affect on a person's health, and worse than that the affect is on someone else's life because they are too young to be able to make their own informed choice.
In a nutshell, no, not dangerous. Even if it turns out that I am wrong and things like GPS and mobile phone satellites are faked and actually work through someway on Earth, then it still does not make a difference to my life. They still work, just not in the way I am told they work
I think my concern about FET being dangerous is cherry picking which mathematics are acceptable and which are not. For example, is it be acceptable (or safe) to dispute the mathematics of the sub-c Newtonian theory of gravitation and circular motion yet accept the mathematics of a sub-c amusement park ride exhibiting the same motion is true? This is surely a paradox: a person who designs a safe amusement park ride surely cannot also believe in FET - or how could he/she actually believe in their own calculations? The mathematics predict the same outcomes!
On a more philosophical level, challenging established scientific theory is healthy, important and inherently safe - as theories can be hypothesied, tested, repeated (or not) and accepted or refuted. The problem with FET is that there is only a hypoetheis. There is no repeatable, achievable experiement to accept or refute. Why? Because like all conspiracy theory, any evidence disputing accepted science is simply rubbished as fabricated, conspitorial and more paradoxically - proof of the conspiracy!
Even a man who was watched ascending in a balloon to 128,000 feet with clear curvature filmed by several cameras is disputed by FET. This was funded by a soft-drink company. Not a govement, not an agency, not a party with a conflict of interest or a confirmation bias - just a record-breaker did it purely for that reason. The many cameras also showed a spherical earth. The Baumgartner also saw the curve. But this would be disputed as "lens aberration" and "lies" respectively. And that's my point in a nutshell.
Thus the danger of FET? Any evidence or repeatable proof offered to contradict FET is simply labelled "conspiracy", "lies", "faulty measurement" etc. or weak alternate and non-provable theory (e.g. observable GPS satellites being "high altitude planes - possible solar powered"), with no counter-evidence to prove the theory.
Hypotheses, like "fairies at the bottom of the garden", without testable and repeatable evidence, that vehemently refute tesable and repeatable evidence, risk underminging human scientific endeavour on many so levels.