How do those who believe or ascribe to Hypostatic Union interpret Philippians 2:7?

"Does he mean God "puts aside" his divine attributes when he takes the form of Jesus?"

No.

This is much related to the glorification of Jesus in John 17. As opposed to Paul's alluding of the putting off of glory when he says that Christ "emptied Himself, taking the form of a slave, becoming in the likeness of men," and was "found in fashion as a man"(Phil. 2:7-8).

And now, glorify Me along with Yourself, Father, with the glory which I had with You before the world was. (17:5) I have glorified You on earth, finishing the work which You have given Me to do. (17:4)

Glory is ontologically the mode of the Divine Being in which God manifests Himself. In the Old Testament God's people could, at most, look upon the glory. The prophets introduced the notion that in the future the glory of God will be an enduring reality that will fill the earth, but even then the glory is only with God as the expression of His manifest Being dwelling among humankind.

Ramm, in his book, "Them He Glorified: A Systematic Study of the Doctrine of Glorification", observes that "it is a kind of totality of qualities which make up His divine power," and he concludes:

the glory of God is not...a particularized attribute like the wisdom of God but an attribute of the total nature of God, virtually an attribute of the attributes”.

It is in the person of Christ that the ontological and eschatological aspects of glory meet, for in Him we behold the God of glory and in Him we shall be glorified. The Gospel of John is especially concerned with this theme. In fact, we can easily define the sub-theme of this Gospel as the incarnated Glory of God on the path to bringing His believers into the divine glory through death and resurrection.

The opening words of both the Gospel of John and the Epistle to the Hebrews refer to the Son in His eternal existence as glory. The Son eternally exists as the expression and glory of the Father, and the distinct function of the Son is to make the Father manifest. The son is identified as the glory of the Only begotten of the Father (1:14). By this we should understand the hypostatic nature of glory in the Godhead—glory not merely as an attribute of God but as the unique hypostasis of the Logos as the expression of God.

We cannot construe this emptying - the so called kenosis (from the Greek verb for emptied here) as a putting off of His divinity in toto; otherwise, He would not have been God at all during His earthly life, and His death on the cross would have lost its redemptive efficacy.

Rather, in simple terms, after the Lord became flesh, He expressed God to some extent, but the glory of God, the glory of all His attributes, was hidden in His flesh. The glory of all God's fullness was covered, being clothed by His flesh [i.e. emptying]. It was revealed once on the Mount of Transfiguration.

Thus, Jesus told His disciples that He had to die and be resurrected. This is liken to the glory and beauty of the flower that are hidden in the seed are released by its death [c.f. John 12:24].

The "colorful beauty and the rich glory" are released through death and resurrection. This is glorification. After the Lord told His disciples about His impending death and resurrection, He offered a prayer to the Father, praying that the Father would glorify the Son that all the glory hidden within Him might be manifested through His death and resurrection. To glorify the Son means to bring forth all the glory hidden within His flesh, to release by means of death and resurrection all the divine glory concealed within the flesh of the Son.

Typologically, just as God’s shekinah glory was concealed within the tabernacle, His divine element was confined in His humanity.