I think what I've found with sessions is that they are very individual and can vary quite a bit on what might be acceptable. As far as I've heard (I'm afraid I've not got there - I can't travel 20 miles often in a week and "prioritise" according to my musical preferences), you would be more likely to get "told off" for as maybe as a one off inserting something not English in the English session than you would for inserting something not Irish in the Irish session which takes place in the same pub (and I have played a couple of Welsh tunes in that one). Another Irish session I go to is stricter...

Of course, re the tunes, (as I think you noted before?) there is some crossover anyway - some are just played differently.