I really sympathise, Challenger.
I knew in advance that one relative (not my wife) is a hard-core anti-masonic nut, so I avoided arguments simply by not telling her. To make sure that no-one else would tell her, I also had to avoid telling any other relative except my wife. Fortunately my (then-)wife came from a masonic family, so she was very supportive. So far as I'm aware, the relative I couldn't tell still doesn't know, and she lives a few hours away so there's a reasonable chance that she won't find out. There'll be a terrible argument if she does find out.
Of course, this doesn't help you, Challenger, since your family already knows you plan to join. I suppose the way to handle it depends on what sort of relationship your have with these relatives. My gut reaction with religious objectors is to tell them the truth, which is "All the stories you've been fed are lies and frauds, you know nothing real about freemasonry and are speaking in ignorance against good men and true, so all your objections are complete rubbish, and you ought to pray for forgiveness". However, of course I've never been faced with the prospect of saying that to family, which would obviously be very awkward. The not-enough-time objection perhaps deserves more serious discussion, if there's any chance that it might be true. Freemasonry does take up time, especially at first when you're learning.
If one of the objectors is your wife, then don't join unless you can resolve her objections, we really don't want to be a source of dispute between man and wife. If your wife (if you're married, I don't know) is okay about it, then you could legitimately consider ignoring the objections of the others, provided you're satisfied that they're wrong. Nevertheless, try to figure out how badly they'll take it and what impact this might have on your family relationships. If it looks minor, then go right ahead and join, they'll get over it and come round later when they see what a good thing it actually is. If it looks so bad that it'll break up the family, then heck, we don't want to be the cause of that, don't join. Somewhere in between, well, judgment call ... good luck.
Best,
Huw