(As you might expect, this answer contains swearing.)

In the era you refer to, both of these things are true:

1.) people were more wary about swearing in public spaces (including in print)

2.) soldiers swore a lot

Oh Kaiser Bill is feeling ill, the Crown prince he's gone barmy,

And we don't give a fuck for old von Kluck and all his fucking army.

-- From a WW1 song

I'll focus on WW1 since that's what you mention. But a little context first.

Swearing and ribald jokes were considered quite masculine, and not suitable for feminine ears or eyes. Anything in print, of course, could violate such terms, which means the evidence we have tends to be very scattered, as things spoken in the privacy of men did not got transcribed for public viewing. As an example, the current record for first known Uranus joke is 1859 (the name of the planet was coined around 1850). Amongst a meeting of important British male society, the joke was made "apropos of nothing":

If you put your head between your legs, what planet do you see? Uranus.

The meeting was later put into print in the publication Punch, but the joke was changed to an entirely new one (as I've written about more here). The reason we know of the actual joke told at the time is it made it into the diary of a person who was present (Henry Silver) and the diary was studied recently by a researcher into Victorian humor.

Sailors and soldiers often were in male-dominated spaces, and a 1795 work (Reflections on Profane and Judicial Swearing) notes that there were two groups "addicted to a wanton profanation of God's holy name; to swearing for amusement, and blaspheming; I mean our Soldiers and Sailors". We can trace links even farther back to the 15th century as the English often called their opponents in the Hundred Years' War goddems.

Regarding WW1, we have the usual expurgation of most texts (letters home, for instance, often did not contain the profanity being used in the trenches) although we do have an memoir titled Her Privates We published by "Private 19022" (those are Shakespeare references) including this passage

“Your language is deplorable, Martlow,” said Bourne in ironical reproof; “quite apart from the fact that you’re speaking of your commanding officer. Did you learn all these choice phrases in the army?”

“Not much,” said little Martlow derisively; “all I learnt in the army was drill an’ care o’ bloody arms. I knew all the fuckin’ patter before I joined.”

This memoir escaped the censors due to being an anonymous limited run (and an expurgated version was published after). While the memoir was fictionalized, we know in general that "fuck" in particular was quite common in WW1. "Fuck", "bloody", "balls", "shit", and "bugger" had "ing" added as needed.

...‘fuck the fucking thing. I’m going to fucking well stay in the bloody hole.’

-- Brooke Claxton, future Canadian minister of national defense, characterizing the British attitude to trench warfare in a letter

As implied above, some of the swearing got out, as a certain Robert Gordon Brown of Quebec had to apologize to his mother, circa 1918:

There is a host of so-called slang expressions which have come into common use among the soldiers, many of which will be retained in our vocabulary, I should say to its loss. We are all too apt, as you know, to incorporate into this language of ours, new and uncouth expressions which only go to make it more impure and complicated.

The historian Cook notes that the adoption of some slang may have helped with language barriers, as there were enough languages mixed together during the war that slang became a standardized way to communicate. This means it is possible some of the casual swearing use was not just regular macho projection, but a way to indicate internationally-understood messages. From Songs and Slang of the British Soldier, 1914-1918 published in 1931:

...[Fuck was] so common indeed in its adjectival form that after a short time the ear refused to acknowledge it ... by adding -ing and -ing well an adjective and adverb were formed and thrown in every sentence. Thus if a sergeant said "Get your fucking rifles!" it was understood as a matter of routine. But if he said, "Get your rifles!" there was an immediate implication of urgency and danger.

The text doesn't actually put "fuck" there, it censors it, since the excerpt was published in 1931. There are no standard dictionaries that even list the word from the span of 1728 to 1965.

...

Cook, T. (2013). Fighting words: Canadian soldiers’ slang and swearing in the Great War. War in History, 20(3), 323-344.

Hughes, G. (2015). An encyclopedia of swearing: The social history of oaths, profanity, foul language, and ethnic slurs in the English-speaking world. Routledge.

Nicholson, B. (2020). ‘Capital Company’: Writing and Telling Jokes in Victorian Britain. In Victorian Comedy and Laughter (pp. 109-139). Palgrave Macmillan, London.