You could totally refuse to do parents' evening if it is on your non-working day. However, I think they would probably be justified in asking you to communicate with the parents another way. For instance, if you share a class, you might brief the other teacher on progress in the bits of the curriculum you've covered, or in secondary, they might ask you to respond by email/telephone to any questions from the parents that couldn't be answered by the head of department. The time for that would still have to come out of your directed time budget, but it might still be a lot easier to do the parents evening!
If you are considering agreeing to anything that is on your non-working day, then you can point out that you are not obliged to attend, although you can see that it would be useful to do so, so you are willing to attend if they are willing to pay you for the extra.
Your directed time should add up to the correct proportion of 1265, but it doesn't have to be the right proportion of each type of activity. So, for instance, you might do more parents evenings and fewer break duties or staff meetings.
Also, sometimes schools say that if you are 0.6 you have to do 3/5 inset days even if they are all on your non-working day. That is not true; if the inset days are all on your non-working day, then you will almost certainly be teaching more than 3/5 of teaching days. they can't have it both ways!
In my experience, where schools know the rules and don't try to force part-timers to do more than they should or to work on non-working days, part-timers are rather more likely to flex when asked nicely, and given some pay or time in lieu.