AND NOW, ONTO āACTUALā CLONE CULTURE (aka I have been provided with an opportunity to yell about Jedi and Clones and dammit I will use it)!
TCW does address this question of what inspired the Clones as they built their identities. In Fivesā arc, Nala Se says this:
NALA SE: Iām afraid the Jedi have inspired creative thinking in some of the Clones. That is the cause of this type of divergent behavior.
We also see that a huge influence on the younger Clone troopers is Shaak Ti - sheās the one who teaches Echo and Fives the importance of unity, tying her own understanding of it directly to her identity as a Jedi.
We see Yoda teaching the Clones that they have value at the beginning of the war:
YODA: Come, sit. Your helmets, remove them. Your faces I wish to see.
THIRE: Thereās not much to look at here, sir. We all share the same face.
YODA: Deceive you, eyes can. In the Force, very different each one of you are. Rys, always focused on the enemy, are you. For inspiration, look to yourself, and those beside you. Jek, concerned about weapons you are. Weapons do not win battles. Your mind, powerful it is. Outthink the droids, you can. Thire, rush not into fights. Long is the war. Only by surviving it, will you prevail. Yes. Clones you may be, but the Force resides in all life forms. Use it, you can, to quiet your mind.Ā
And we see Plo do the same in the very next episode:
WOLFFE: Weāre just Clones, sir. Weāre meant to be expendable.
(By this point the Clones already have tattoos, painted armors and unique haircuts, but these are superficial ways of expressing your identity. Itās illustrated very clearly with the episode Innocents of Ryloth. Boil has a mustache and a Death Watch symbol on his helmet. Great! But he spends most of the episode griping about the hassle of protecting civilians, and using his duty as a soldier as an excuse not to take care of Numa. With the combined influences of Waxer, Obi-Wan and Numaās delightful nature, Boil actually shows who he is by the end of the episode: a deeply caring man. Thatās who is is, more than anything else. When Numa hugs him, he has his helmet on but sheās not afraid of it anymore. Because his face isnāt synonymous with who he is, no matter how ācustomizedā, his actions are who he is.)
tldr: weāre told that the Jedi are the one who most fostered unity and creativity in the Clones.Ā
(Again, visible in Innocent of Ryloth, when Obi-Wanās influence makes his men appreciative of TwiāLek culture - he even teaches them a Ryl word). Decades after the war, the GAR is remembered as the Jedi and the Clones (see Hera reminding Kanan of the bond between Jedi and Clones in The Lost Commanders.)
Also, remember the remembrance thing fics are so fond of using?Ā
Ni su'cuyi, gar kyr'adyc, ni partayli, gar darasuum - āIām still alive, but you are dead. I remember you, so you are eternalā
Nu kyr'adyc, shi taab'echaaj'la - āNot gone, merely marching far awayā
Guess what? The Jedi had memory moths in the pre-2009!TCW EU.Ā
You whisper a name to the moth and it repeats it forever.Ā
And actual canon has so much stuff about not actually being dead but passing into the Force, and just being on a path everyone will eventually walk, yada yada yada.Ā
LUKE: I canāt do it, Artoo. I canāt go on alone.
OBI-WAN: Yoda will always be with you.
YODA (s5ep18):Ā One with the force, they are. And our job it is
to remember that we will, in time, also pass on. Luminous beings are we, but temporary vessels, our bodies are. And we shall all find ourselves
here in time. A moment of silence, I ask, to remember and to move on.
So even fanon Clone culture is directly linked to the oldest and most basic Jedi principles.Ā
So if the Clones actually had traditions and philosophical/theological views in canon, theyād more likely to be inherited from the Jedi than the Mandalorians. No one in TCW states a connection between Clones and Mandalorians (not Maul, not Bo-Katan, not the Jedi, not Satine, not Almec, not Boba, not Hondo, not the bounty hunters, not the Republic authoritiesā¦) but TONS of what we see in the Jedi/Clones interactions points to Jedi culture being a HUGE influence on the Clonesā way of expressing themselves.Ā
Last little note: Jedi culture is hugely emphatic on the irrelevance of where you come from compared to who you decide to be. While the Jedi have nothing against embracing your birth traditions (see their various traditional clothes, tattoos, jewels, their different accents/languages, their acceptance of other faiths - see Barrissā prayer statue - and the fact that they keep the names given to them by their biological parents), not all Jedi feel the need to identify with their biological people, their identity is rooted in their role as peacekeepers, as they routinely states, and in their connection to the Force and their fellow Jedi.Ā
Similarly, the Clones have different views on whether or not their origin defines them, some express themselves with alterations to their appearances, some donāt, and their sense of identity is most commonly rooted in their role as soldiers, their loyalty to the Republic, and their brothers.Ā
Clone culture draws on Jedi culture.
Great overviews of the Jediās relationship with the Clones can be found here (gifs from @laciefuyuā) and hereĀ (āYour Body and Your Blade,ā amazing fanvid byĀ @trickytricky1ā)