Because I had no symbol specific to co-Masonry, I asked for suggestions. Somebody suggested the logo of Universal co-Masonry.

This logo has a few typical / recognisable elements. I had thought to add the Le Droit Humain logo (and derivatives). How many elements actually are typical / recognisable? A little bit of digging.
The oldest version of the Le Droit Humain logo that I could find comes from the 1895 Bulletin.

It looks quite a bit like this (from 1918):

As you can see, the (acacia) branches are already there, the square and compasses and the star in the middle. The uneven square, which was to become fairly typical, is not yet present. That did appear in 1908, also in the Bulletin, together with the G in the star. Maybe to take a step away from the Grand Orient de France design?

This was going to be the recognisable logo for Le Droit Humain for many years to come and around the globe. The square has uneven legs, a G appears in the star. Also notice the ribbon at the bottom of the square. Up until today, many federations of Le Droit Humain still use this logo.

From The co-Mason (UK, 1910).

The Dutch Bulletin of 1918, which is the same as in the Finish Yhteis from 1921. Etc. Etc.
Sometimes the text has been translated, like in this old, American logo (The American co-Mason 1930).

But which elements of this logo are ‘obligatory’? Not many!
You can see that the left arm of the square is longer than the right one. The French federation at some point turned that around. Plus, the ribbon is gone.

Is it the star in the middle then? Again not, look at the international logo of Le Droit Humain of today.

As if they follow the minimalising trend set by the United Grand Lodge of England. You also see that the branches have disappeared.
The branches have also disappeared. Still they are a recognisable element. Here is the logo of the Greek federation, which has replaced the G by the Greek Gamma. The branches are different, but the combination of the branches and the uneven square, make this a recognisable Le Droit Humain logo.

Also other federations have modernised the logo, such as the Spanish federation.

Which is still recognisable, but what about this Austrial federation logo?

Some elements are still there, but if the square would not have read “Le Droit Humain” it might not immediately have seemed like an LDH logo.
The British federation also has a modernised logo on their website.

The G, the branches, the star moved to the text, the square became even. The elements are still there, but this logo is not immediately recognisable as Le Droit Humain anymore in my opinion.
As for Universal co-Masonry.

They have kept the recognisable elements, the uneven legged square, the branches, the star, but the G was replaced by a Yod.
I guess an emblem that has retained most of the elements of the 1908 French logo can be regarded as fairly typically co-Masonic, but not so typical that everybody wants to keep them.