When you are talking about mechanics this means a 2 point decrease in your primary ability and the loss of a feat that synergizes with your class abilities and replacement with a Feat that is of little value for your class.
Constitution is not nearly as important as Dexterity for numerous reasons.  the PHB even says explicitly that Dexterity and Wisdom are the primary abilities of Monks and when you get down to it, Wisdom is not as important as Dexterity.
No they are not sky blue.
There are 16 backgrounds in the PHB.  For a Monk Acolyte and Sage are number 12th and 13the out of 16 respectively.  If Sailor is gold, Wayfarer is Sky Blue, Guide is Blue, Scribe is Purple and Criminal is yellow, Acolyte and Sage are red or "F" or whatever.
The two backgrounds that make the most sense thematically for a Monk are among the worst you can choose.
Exactly, and this is why they should not have mechanics like ASIs or feats attached to backgrounds, the backgrounds are there for story and having these elements gets in the way of the story hook.