Hi Dragana,

Both the future and the subjunctive are given as possibilities. In the case of -

J'espère que tu puisses me pardonner 

there is a doubt that this will happen.

With espérer que, it is all to do with the degree of doubt implied.

Take a look at a similar question and the answer given which you might find useful :

https://kwiziq.learnfrenchwithalexa.com/questions/view/esperer-que-and-the-dreaded-subjunctive

Bonne Continuation!