What would happen if a gifted member of a hedge tradition that grants Favored Abilities is initiated into another tradition that also grants Favored Abilities and has its arts succesfully opened again?
For example, a Muspelli summons its patron to open the arts of a Folk Witch? Would the Folk Witch replace its favored abilities with these of her Patron, therefore lowering her amount of Favored Abilities from 7 to 6? Replace some of her Favored Abilities with these of her Patron, remaining with a total of seven with some of her former favored abilities considered as normal abilities? Or does she gain six new favored abilities, to a total of 13?
For Divine or Infernal traditions it would have been easy to answer, since for them it is explicit that you can only ever gain the Favored Abilities benefit from one single tradition.
No equivalent rule exists for Magical traditions that I know of, so you'd probably get all the Favored Abilities of both traditions - but do keep in mind that opening the Gift for the second tradition such that existing Arts and Supernatural Abilities are retained will probably require a very high Opening Total.
If the opening total is only just high enough, the character will lose all existing Arts and Supernatural Abilities. (All per the usual rules for Opening the Gift.)
The Muspelli are a bit special in this regard since it is the Patron which does the actual openening, and they don't have a specified Opening Total.
One point to note is that having a Favoured Tradition only removes the penalty for learning other abilities in that tradition (Hedge Magic pg 9). So even if you could have two sets of favoured abilities, they'd interfere with each other.
They wouldn't interfere at all. You have not penalties to learn A, B, C. You have no penalties to learn X, Y, Z. So you have no penalties to learn A, B, C, X, Y, Z.
Note that Favored Abilities are not telling you what Abilities/Arts cause penalties, but what Abilities/Arts receive penalties. This is the whole idea of the Gift being Opened to a second tradition: it's very hard to accomplish (as ErikT noted), but then you can learn each tradition's stuff with no penalties.