Do you say Los avestruces or Las avestruces?
I think I've seen both. Maybe both are accepted?
In singular it is easier, and maybe it just extrapolates to the plural. In singular it's El avestruz, in order to avoid two identical vocals together.
Just to complement the good @AlexisPigeon answer, I want to make it clear that it's not
el avestruz "in order to avoid two same vocals together" -which is known as cacofonía- as you said in your question...
That happens with some feminine nouns such as
el agua or
el hacha, but in this case it's just because
avestruz is a masculine noun and that's all! If you see
las avestruces, it's just wrong...
"... in order to avoid two same vocals together."
You're a bit wrong here about the rules to apply in order to avoid cacofonía. Even if avestruz were female, the proper way to write it would be "la avestruz". In order to apply the "cacofonía avoid rule" (sorry for the expresion invention) you need two conditions:
For example, you have to say "el hacha" and "el águila", but on the other hand you have to say "la apertura" (the accent is in the "u") and "la ambrosía" (the accent is in the "i").