Les tatouages ont toujours eu des connotations mixteambiguës dans mes cercles procheson entourage.

"Mixed" would be a false friends here. "mixed connotations" would be "connotations ambiguës"
All people surrounding you are called "l'entourage"

Je suis chrétienne, donc, c’est très récemment que j’ai pris le temps de réfléchir/méditer sur le sujet des tatouages.

faire quelque chose réceMMENT ("recentLY", adverb)
"méditer" would perhaps be a little too strong in this context

Selon à moi, jJe les trouves très inspirants quand- ils otransmettent des messages profondes et avec l’intention.s, [avec une vraie intention derrière ?]

selon moi (that would be redundant since you already have "je les trouve", which indicates an opinion)
Masculine plural agreement => inspirantS
"transmettre un message" would be more accurate and natural
Masculine plural agreement with "messages" => profondS

I'm not sure I've grasped the end: if you meant you find them inspiring when it was their bearers' intention to transmit a message, in a pinch you could say "avec une vraie intention derrière" so it's clear, but you can drop it since it's pretty much implied in "transmettent des messages profonds"
Even better => quand les gens qui se font tatouer ont une vraie intention de transmettre un message profond

Ils ont l’opportunité d’être le début d’une conversations très vastesreprésentent une opportunité de démarrer/d'entamer/d'initier une longue conversation avec un inconnu.

Only people who can act "ont" ("have") an opportunity; you can however say tattoos "représentent" ("represent, constitute") one

"un sujet" ("topic") can be "vaste" when there are many points to consider and aspects to discuss, but "une conversation" (without a <s>, singular) would be "longue" or "grande"

Although it's right, "initier" would probably the least common verb with "une conversation": "démarrer" or "entamer" would definitely be more common

I've made some other changes so the sentence looks more natural