If wormholes exist and behave like we think they do, can we cross them without "negatively charged matter "? I heard and read that a wormhole will collapse if they transport any positively charged matter. So, if wormholes exist, they probably close as soon as normal matter enters it, how can we access them without negative matter?
The best current answer is "We can't".  We do not presently know of any way to stabilize wormholes without large negative energy densities. (Some argue that even that isn't enough, but I don't believe that the matter is settled, even on a theoretical level.)

Note that:

(a) No wormhole has ever been observed, nor have we observed anything which is a predicted effect of a wormhole: Wormholes are entirely theoretical.

(b) Having said that, Wormholes are a prediction of General Relativity, which is a very well-tested and well-established theory, so it's unwise to bet against them existing.

(c) Macroscopic wormholes are a purely GR phenomenon and while the fields involved are strong, they are not so strong that they are in the realm where we expect the eventual unified theory of quantum gravity to give markedly different results.

(d) And by the way, we haven't a clue how to create large negative energy densities.