What is your budget for giving money to your parents? If you move in with BF, does that change as you are now having different expenses and perhaps saving towards other goals?

Your budget should reflect how much you have/put in the shared account. Nothing else should be in it, only what you give to your parents as gifts (or shared bills). It should also be an amount that do not take away from your other goals - be it food, furniture, rent, clothes, hobbies, retirement, travel, car, haircuts (and on and on the list goes). I would not be surprised if BF refuse to have merged financial situation with you until you've set an amount that does not mean he too supports your parents to the detriment of his own goals. He shouldnt. You shouldnt.

If you want to help, help. But do so with open eyes and in a way that does not hurt your own financial situation or your BF's.