Or maybe it's a handmade mug made by several people entered into a contest. ;)
Why is the plural mugs translated as singular? I think this is wrong in both languages. "Your mugs are red" and "A ti bögrétek pirosok" maybe?
Or we can say that, when there is a plural possessor and a singular possession ("a ti bögrétek"), it is somewhat ambiguous. We can not be sure if it is one possession shared by all or each having one to their own. It depends on context and the actual things we are talking about. For example:
"A ti fejetek piros." - Hopefully, we are talking about each person having their own head(s?). :)
In any case, yes "bögrétek" is grammatically singular, so it has to go with "piros", not "pirosak".
Also, when having both plural possessor and possessions, we cannot be sure of the ownership arrangements:
"a ti bögréitek" - this is definitely several mugs, but we don't know if they are collectively owned or everyone has several mugs. Again, it depends on context, and may need further clarification. For example:
"a ti szüleitek" - definitely talking about everyone having multiple parents. But if these people are siblings, then they also share the same parents.
Soi DUO should stop giving us ambiguous sentences to translate, or supply context for whatever is ambiguous. Unless, of course their intent is to make us learn from our errors, but I don't think so. I think they are making errors accidentally.