I think that El touching the monster accomplished a couple things, in addition to creating the initial portal. First, I think the monster was not aware of the parallel world before that, if the world was even "that" parallel before the touch.
But more importantly, the touch and El's reaction generated sufficient energy to align the worlds (think of Mr Clarke's folded paper example). After this event, at times, people in the same place in the real and upside-down worlds could sometimes hear and/or sense one another.
To me, this indicates such a close association between the two dimensions, that the monster -- especially when sensing blood -- can create new ways to cross that barrier.
I wouldn't necessarily call the monster's crossing effortless; we've seen a couple times when it had to make some effort to get through a wall or ceiling. Though the passage through the tree was different somehow; I'm not sure why.
Also, recall the scene where Will was able to get close to coming through the wall in his house (the place where Joyce subsequently took an axe to). Perhaps the only difference between Will not being able to actually break through, and the monster being able to, is strength. We are told that the atmosphere is poison to humans and we see Will's weakness, but he still got kinda close.