"We have no dogs due to the fact that we are against animals."
Translation:Wij hebben geen honden, doordat wij tegen dieren zijn.
"Doordat" is used in cases where something(out of your control) causes a situation and it wasn't obviously your intention to let that happen.
I couldn't make it on time, because(omdat) I didn't know what to wear. (Worst pretext ever, I know :P)
I couldn't make it on time, because(doordat) my flight was delayed.
I hope you'll understand.
Dat is niet wat deze website voor nederslands sprekers geven: http://taaladvies.net/taal/advies/vraag/598/omdat_doordat/
NO, "Staan tegen" exists in dutch, but it means "standing against" in the meaning of fysically leaning against something, like a bar or a wall. In English: Standing up against something is like a revolution not a fysical thing at all. In Dutch there is a word like: "Opstand" fysically meaning standing up an translated into English like: "Rebellion, revolt, rising". So you were close, sorry :)