I believe it to be both intellectually and spiritually unhealthy to spend your time in end times speculations. It is far better to live your life in such a way as to make this world a better place not just for the present but into the distant future.
I'd be inclined to suggest it's unhealthy
not to at least be aware of times and seasons. I agree it's unhealthy to get obsessive about whether this or that thing is the mark of the beast, or whether this or that person is the antichrist or whatever else but it doesn't hurt to at least observe patterns and trends.
Of course there's a difference between watching patterns and trends as a sideline and spending more and more time poring over the fine details of the Revelation trying to prove that the sky is falling.
No arguments about living in a way that makes the world a better place!