I work on a dive charter that runs out of Boston Harbor and also shore dive frequently in Cape Ann (Gloucester/Rockport) so here is my 2 cents.
At least around Boston harbor islands, most of my recent encounters with lobstermen have been mainly positive, provided you're not in the middle of their pot lines while they're hauling. We've helped a few unfoul line from their props or locate lost pots; I figure the good will is a nice gesture.
I simply try not to surface near their buoys if I can help it and I try not hang out "near" their pots underwater if I can avoid it. Just use common sense and common courtesy when anchoring boat. This is easier said than done, especially up in Cape Ann where there is a much greater density of lobster pots.
The rivalry doesn't "seem" as bad as it used to be a while back but there are still some bad eggs out there (on both sides) so be careful.
It can be a little more heated up in Cape Ann where you have a large number of lobster pots and lobster boats. I've had some bad experiences at Lanes Cove and Old Garden Beach but nothing lately in last 2-3 years. While ago I've had lobstermen drop traps near/next to me at Lanes Cove, pull traps up at Old Garden Beach very close to me.
Overall, obey lobster guidelines and measure twice to be safe, anything questionable I throw back. Not worth the fine or risk.
Make sure you've got lobster numbers on your tanks AND dive flag visible. Carry your lobster license (keep in your car if shore diving or on boat). I used to go through trouble of laminating mine and keeping it in my drysuit pocket or save a dive kit; now I just keep it in my car while shore diving.
Most people won't willingly give up their favorite honey holes for lobstering but a lot of shore diving sites up in Cape Ann are good bets for lobstering; I like Old Garden Beach, Bass Rocks, Loblolly Cove, etc. Most will agree you'll have better luck if you have a boat at your disposable or go on some dive charters.
Have fun.