Here is a good reflection by Fr Ted Bobosh, on prayer for the civil authorities. A couple of scriptural and liturgical snippets:
First of all, then, I urge that supplications, prayers, intercessions, and thanksgivings be made for all men, for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way. This is good, and it is acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth. (1 Timothy 2:1-4)
Remember, O Lord, this country and all civil authorities: grant them a secure and lasting peace; speak good things into their hearts concerning your Church and all your people, that we, in their tranquility, may lead a calm and peaceful life in all godliness and sanctity. (Priest’s prayer in the Divine Liturgy of St Basil)
In both of these, the main reason we’re told to pray for the civil authorities (whoever they are and whatever their policies or character) is that they may allow the Church to function in peace. Increasingly, this is about all I hope for from the secular authorities.