I doubt anyone here can answer this yes or no, since it depends on so many factors.  Also, it's not clear whether you rent or own, which is huge.  But I would do everything possible to change this. 

Even if you rent, I'd try talking to the neighbors first and explaining why you object to this. Is it possible the camera doesn't even capture your portion of the back yard?  You just want to be sure about that stuff.  If they act like jerks or won't show you what it captures, get the landlord involved.   If this is installed in front of YOUR garage, landlord should be willing to tell them to remove it.  

Check with your landlord/manager first.  A renter can NOT install security cameras without permission from the landlord/manager.

He cannot position a camera so that it views property that is exclusive to you. He can cover shared areas.

The camera is legal since you have no expectation of privacy when you are outside of your dwelling.

DEAR GOD!!! Do you know how to spell?

**Our garage is next to there’s [THEIRS] and are [OUR] back yards are also split. One of the cameras was installed right in front of our garage and it makes us uncomfortable when we are back there having a bbq or just been [BEING] in our yard.**

Learn to spell and you will look like less of a fool.

The question is more what do they do with the information.

If they publish or distribute it, 'as a recording' then you might have defamation grounds.

You would have to check your local legal support / police if there are privacy violations - but sounds like it is already considered a publicly visible and accessible area - so not likely therefore.

yes................................

Your have no expectation of privacy in your backyard, thus the camera is not illegal.

Yes, they are allowed to do that.