I think the four categories are:

Words containing "SKI"
- ESKIMO KISSES
- BASKIN ROBBINS
- SKINNY DIP
- MINISKIRTS

Things with POLES
- BARBER SHOPS
- STRIP CLUBS
- MAGNETIC FIELDS (north and south pole of a magnet)
- POLAND

Things related to LIFT
- PLAGIARIZE: plagiarized text is lifted from the original source
- REMOVE WRINKLES: accomplished by a facelift
- ELEVATOR CABLES: used to lift the cab (and the elevator itself is called a lift in some countries)
- JOINT ROTATIONS: movements used in lifting weights

Things that are GREEN
- LILY PADS
- ENVIRONMENTAL GROUPS
- WREATHS
- TAKE THE ROPES: seems a bit iffy, my best guess is that a newbie, who is "green", has to learn the ropes

The common connection is

Skiing: Ski (duh), ski lift, ski pole, and finally the color green used to denote beginner ski slopes

I think the four categories are:

Words containing "SKI"
- ESKIMO KISSES
- BASKIN ROBBINS
- SKINNY DIP
- MINISKIRTS

Things with POLES
- BARBER SHOPS
- STRIP CLUBS
- MAGNETIC FIELDS (north and south pole of a magnet)
- POLAND

Things related to LIFT
- PLAGIARIZE: plagiarized text is lifted from the original source
- REMOVE WRINKLES: accomplished by a facelift
- ELEVATOR CABLES: used to lift the cab (and the elevator itself is called a lift in some countries)
- JOINT ROTATIONS: movements used in lifting weights

Things that are GREEN
- LILY PADS
- ENVIRONMENTAL GROUPS
- WREATHS
- TAKE THE ROPES: seems a bit iffy, my best guess is that a newbie, who is "green", has to learn the ropes

The common connection is

Skiing: Ski (duh), ski lift, ski pole, and finally the color green used to denote beginner ski slopes

However, as Stiv noted in the comments this answer is probably incomplete:

Both POLE and SKI can be followed by synonyms for LEAP (pole vault and ski jump); given this was posted on February 29 aka leap day, that seems like it's probably the intended connection. If anyone can extend this idea to the other categories feel free to post it in a separate answer!