Potential Spoilers below:
Wonder Woman: featured a Native American "Chief Napi" who's able to navigate through No Man's Land and trade goods with both sides of the war (such as German beer for the British and British tea for the Germans).
The Lost City of Z: featured an elderly Russian female psychic who was smuggled into an English trench to give palm readings to soldiers.
For Wonder Woman, the Chief was warmly welcomed by the Allied troops who see him, seemingly like a regular visitor. Were civilians (and otherwise non-authorized people) able to freely visit soldiers in the trenches like this, whether or not they provided goods and services?
These sorts of things are really nothing more than useful plot devices, I'm afraid (as, incidentally, is Wonder Woman's portrayal of a fully functional village, complete with convivial cafe, in a tight salient apparently within a few yards of the front line).
The trench systems that were developed during the war were designed to do one thing at all costs - prevent a decisive enemy break-through into open country behind the lines. A secondary function was to make effective counter-attack possible. In the sort of fully developed systems typical of the latter phases of the war - as depicted in Wonder Woman - both these imperatives resulted in the constructed of multiple lines of trenches, in which the most forward trench might often be relatively basic and only lightly held, but which would be backed by secondary trench lines with dugouts, more troops and so on. At some distance behind this front line complex there would be a significantly larger, better and more strongly fortified series of reserve lines, and behind those there would be a third layer of support trenches, often extending nearly half a mile behind the front line. Further back still were artillery positions, headquarters and so forth. These defences were joined by communication trenches.
The idea that an unidentified, miscellaneous group, perhaps including women, could make their way through such a complex set of heavily-manned defences without being stopped and challenged is sadly pretty untenable.
Similarly, any attempt to cross over to enemy trench lines to barter goods would likely end in disaster, since the enemy were generally on high alert for grenade-wielding raiding parties and would be highly unlikely to let any unfamiliar enemy approach close enough to make their business known.
All that said, interesting legends certainly did circulate, during the war and after it, concerning groups of deserters who supposedly banded together to live in nomansland and abandoned portions of the trench system in quieter sectors.Such groups, supposedly, emerged at night to scavenge food and equipment from both sides. The British officer Oswald Sitwell, for example, wrote of the Armistice period:
For four long years . . . the sole internationalism—if it existed—had been that of deserters from all the warring nations, French, Italian, German, Austrian, Australian, English, Canadian. Outlawed, these men lived—at least, they lived—in caves and grottoes under certain parts of the front line. Cowardly but desperate as the lazzaroni of the old Kingdom of Naples, or the bands of beggars and coney catchers of Tudor times, recognizing no right, and no rules save of their own making, they would issue forth, it was said, from their secret lairs, after each of the interminable checkmate battles, to rob the dying of their few possessions—treasures such as boots or iron rations—and leave them dead... the General Staff could find no way of dealing with these bandits until the war was over, and that in the end they [the deserters] had to be gassed.
There seems to be no evidence that this essentially literary trope was based on any real incidents.