A far as I know, we can use SHOULD in a that-clause (after 'be' + adjective) when we talk about our own reaction to something we are reporting after a number of adjectives describing feelings, e.g. amazed, anxiuos, astonishing, concerned, disappointed, funny, interesting, natural, odd, strange, surprised, surprising, typical, upset, etc.
The difference lies in our attitude toward something - if we want to sound more emphatic, or when we want to be formal, we use SHOULD then. However, we leave out SHOULD in less formal contexts. Cf.
It's strange that he should be late...
OR
It's strange that he is late...
To dziwne, że się spóźnia...
I was surprised that he should say such a thing.
OR
I was surprised that he said such a thing.
Byłem zaskoczony, że coś takiego powiedział/że mógł coś takiego powiedzieć.
I am concerned that he should think I did it on purpose.
OR
I am concerned that he thinks I did it on purpose.
Martwi mnie to, że on myśli, iż zrobiłem to celowo.