I’m not sure if you mean the city of Hayward. I am not aware of a Hayward neighborhood except in San Mateo. From your map though, I am guessing you mean the first and not the later.
Here is what I would say about Hayward, the city: it is all relative. Compared to Oakland, Hayward is much safer with lower crime stats in every category. Much safer.
But compared to San Jose to the south, it has more crime. The yearly crime rate is slight above the nationwide crime rate though not significantly more dangerous.
As far as Longman Park goes specifically—I don’t know. What I do know, however, is that there are several Hispanic gangs in Hayward—especially in the north and west of the city. I think you would probably be okay in the park during the day, but I would be leery of being there during the night, I suppose.