It's 60 seconds of your life that you have to be quiet for. Is that really too much to ask for? 
Once a year the country recognizes an individual who played a pretty significant role in developing this nation. Since its a federal holiday, many venues ask for a moment of silence in length of one minute. That's really not asking too much. Its a respect thing.
If you can't take a whole minute of your life to be respecful, you're just being ignorant & self-centered, IMO. Suck it up for 60 seconds.
Please, tell me, what does that 60 seconds achieve, other than giving people wanting 60 seconds of silence a reason to complain if not everyone agrees? They named a holiday after him, they run school programs and history books around the holiday, it's on TV non-stop for a week leading up to it. Those 60 seconds are for NBA marketing, it's the same as a business donating to a charity for a tax-writeoff. Jesus doesn't get 60 seconds of silence on Xmas day. It's marketing.
No offense, but being Canadian, which I'm sure nobody really cares about, you Yanks hand out moments of silence and anthems like they're Celtics retirement banners.
I agree with this post but I also agree with the OP and I would have felt identical to him. MLK owns the minute whether it should be there or not. (I'll bet MLK would say it's not the right time and place for a minute of silence). 1. they could honor him with a shorter moment of silence. 2. they could have no games that day but do a t.v. special with players discussing their feelings about MLK.if they want. If they're going to have games, I would have places in the stadium (inside not courtside) where people can go and read a poster and look at photos..establish his presence and allow for voluntary reflection....but leave out the moment of silence. I would guess players like having it though, and that's where I switch over and think okay, I'll follow, this is how it is and I'm going to shut up for the whole minute and actually honor the person.
The NBA should stick to basketball and curb the marketing schemes and, while I have no problem if they work towards saving the world (the organization and players do a lot of great things and I hope that continues), stop yapping about it every chance they get...It ends up commercialized and feels false. What Stern has no clue about it is the number of people, potential fans, who are turned off by his marketing approach.
I have no real problem with a minute of silence and think people, even big crowds should be able to get all the way through one. But I would choose to honor MLK in other ways if I were pulling the strings.....
That doesn't mean I think less of MLK. What a mammoth figure for the U.S. to be proud of.....