I have a similar position with my DB and niece. Although my DB and I arent completely NC (yet!) he is a nasty piece of work, we have kept in contact for the sake of my mum (who died earlier this year) despite her always agreeing with him, golden child etc.
I have 2 teens and he has done the "I am not buying them presents" thing on and off for years, it is usually when he hasn't got his own way over something or I have upset the poor boy (56, FFS). After a huge fall out 2 yrs ago, he hasn't bought them a Christmas or birthday present since, nor sent cards.
I have always taken the higher moral ground and sent something to my niece. However, this just made my DB gloat, he saw it as me toeing the line, doing the right thing etc whilst he didn't bother! He even went as far as texting me before her birthday last year 'dont forget its her birthday, we expect the same as you send DHs niece/nephew' - yes he is that childish! At 56! I usually got similar comments from my mum, who saw nothing wrong in his actions.
We are now approaching my DN's 21st. Whilst I would like to keep the moral high ground, I am def thinking why should I bother? Yes its a special birthday, but so was my sons 18th last year. My DN got a decent 18th present 3yrs ago, whilst DS got nothing. DS hates his uncle with a vengeance, as he can see what a complete twat he is, so it didnt upset him, but it did me, so why should I keep doing the right thing??
I think in your case, your SIL has made it clear she will never want contact with you again, so why keep up the pretence of happy families with present giving? I wouldnt bother sending anything.