I think it is very easy to believe that "death" and "life isn't usually as wonderful as it could be" are as important as existential risk if you weight heavily in favour of the well-being of you, people you know and people in other senses "close" to you.

Caring more about that is also very natural. If I were to tell a typical person that <person they know> was going to die tomorrow, their reaction would be stronger than <person 10 millennia in the future> is going to die under the same circumstances etc.

Of course, shut up and multiply, but only if you actually care about all of the events equally.