Is Obeying a Stay at Home Order Biblical or Not Biblical

The crucial element is to determine the underlying purpose of the various 'stay at home', 'shelter in place' or other restrictive orders. If the cessation of preaching in the name of Christ is the goal of those orders then Acts 5 is in view. If the various public health agencies have no such ulterior motive then...Romans 13. We need not be a kingdom divided against itself (Matthew 12) and teaching, fellowship, and prayer (Acts 2) are all still possible while the breaking of bread together is awkward but also still possible in one fashion or another.

I think that Hebrews 10:25, in immediate context,

And let us consider how to stir up one another to love and good works,  not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near. - Hebrews 10:24-25

is addressing those individuals who are in the habit of avoiding the assemblage of the brethren and, in the larger context, those individuals are in that habit because of the deceptive nature of sin and, even more specifically, the fear of persecution.

But recall the former days when, after you were enlightened, you endured a hard struggle with sufferings, sometimes being publicly exposed to reproach and affliction, and sometimes being partners with those so treated. For you had compassion on those in prison, and you joyfully accepted the plundering of your property, since you knew that you yourselves had a better possession and an abiding one. Therefore do not throw away your confidence, which has a great reward. For you have need of endurance, so that when you have done the will of God you may receive what is promised. - Hebrews 10:32-36

If believers were not coming together of their own volition because of fear of conviction of sin from within the assemblage or fear of persecution from without then I believe Hebrews chapter 10 might apply. However the stay at home orders and advisories, the business closures and limitations that have been implemented voluntarily and under order are ostensibly for our own good and the good of those with whom we are limiting contact. If we gather together we can infect each other within the church and without the church. Now, depending upon what sort of tinfoil hat one might wear from time to time, one might conceive of an anti-christian power lurking in the shadows of a "stay at home order" and either instigating or taking advantage of this interruption in the Church's gathering together (and one might be correct) but both the 'spirit' and the 'letter' of these human regulations have no obvious connection to the persecution of our or of any particular faith.

If Christians were forbidden to gather while all other groups retained permission then I have no doubt that Acts 5:29 would be a righteous rallying cry:

And when they had brought them, they set them before the council. And the high priest questioned them, saying, “We strictly charged you not to teach in this name, yet here you have filled Jerusalem with your teaching, and you intend to bring this man's blood upon us.” But Peter and the apostles answered, “We must obey God rather than men. - Acts 5:27-29

As it stands, regardless of how opportunistic ungodliness and evil may become, the Christian rallying cry must be something more akin to

Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God. Therefore whoever resists the authorities resists what God has appointed, and those who resist will incur judgment. For rulers are not a terror to good conduct, but to bad. Would you have no fear of the one who is in authority? Then do what is good, and you will receive his approval, for he is God's servant for your good. But if you do wrong, be afraid, for he does not bear the sword in vain. For he is the servant of God, an avenger who carries out God's wrath on the wrongdoer. Therefore one must be in subjection, not only to avoid God's wrath but also for the sake of conscience. Romans 13:1-5

coupled with the overarching command of our Lord and Savior to love God and love our neighbor:

“Teacher, which is the great commandment in the Law?” And he said to him, “You shall love the Lord your God with all your heart and with all your soul and with all your mind. This is the great and first commandment. And a second is like it: You shall love your neighbor as yourself. On these two commandments depend all the Law and the Prophets.” - Matthew 22:36-40

We must not respond from a spirit of fear nor of bravado. Jesus is able to protect and even strengthen and build His church in the midst of difficulty. Indeed, faith is perfected in fire just as gold is refined and, as so many around us slide into fear and despair, who can say how many will be led toward that narrow gate of salvation in Christ by the spirit of God producing the fruits of the Spirit in us through trying times. Remaining in Christ, the true vine, is the key to producing fruit that remains and fruit is not for our benefit.

But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control; against such things there is no law. - Galatians 5:22-23

By the grace of God and His provision of technology we can still lawfully 'assemble' in ways that our forefathers could never have dreamed; we can still spur one another on to love and good deeds, and we can study and pray to have an answer ready for any that ask us of the hope that we have. The one prerequisite is that we must have hope to be inquired. Be of good courage, brethren, the Lord has gone before us and the battle belongs to Him.