I have no end of people asking me if The Vampire LeShoc is the Count from Sesame Street. The two bear no resemblance to each other outside of both being puppet vampires.
We are constantly faced with the inspiration and overwhelming spectre of the Jim Henson brand.
And if we wish to continue to generate puppets in fleece and foam and fur, we will forever be faced with it. Unfortunately, everything most of us do to build our puppets is based in some way off puppetbuilding technology that was pioneered by the Henson Company.
But lets be perfectly clear on a certain point... there is no such thing as copyrighting a "look". Its impossible. If it were possible, Disney would have put every other animation studio out of business for copying their animated character "look". So contrary to popular belief, there is no way for Disney or Henson to sue you for infringement of their "look".
The copyright thing has been argued to death here and elsewhere, so I'd prefer to let the rest of it slide. But rest assured that, unless a reasonable person would easily mistake your work as a copyrighted logo, character or design, you should be able to defend your own intellectual property.
Things to remember: 1) keep a paper trail. Don't throw out your design drawings. MAKE design drawings. Then keep them. Even if the puppet doesn't perfectly look like your design drawing.
2) Don't take your inspiration solely from the Muppets. Look at other puppets, other styles, other art forms. Use what you see. Find your own style of doing things on your puppets. Its nearly impossible to avoid likenesses to Muppets since most of the materials and techniques were pioneered by them. But don't let that limit you.
3) Don't make copies of the Muppet characters to use in your shows or to promote yourself. That's just asking for trouble. Sure... make a replica of Kermit for yourself. Hopefully you'll learn from it and develop your puppet-making skills. Exercise and explore puppet building by doing that. But don't put Kermit in your show and expect it to go unnoticed.