I pray that your partnership in the faith may become effective as you fully acknowledge every blessing that is ours in the Messiah.

So if you consider me a partner, welcome him as you would welcome me.
-Philemon 1:6, 17 (ISV)

Solidarity is defined by as: 
1. Union or fellowship arising from common responsibilities and interests, as between members of a group or between classes, peoples, etc.: to promote solidarity among union members.
2. Community of feelings, purposes, etc.
3. Community of responsibilities and interests.
1840–50; < French solidarité, equivalent to solidaire solidary + -ité -ity

I could not find solidarity in an English translation of the Bible.  So I looked it up in French translations and I found it here, in Philemon twice.  They are the Greek words:
koinōnía (a feminine noun) – properly, what is shared in common as the basis of fellowship (partnership, community).
koinōnós (a masculine noun/substantival adjective) – properly, a participant who mutually belongs and shares fellowship; a "joint-participant."  (HELPS Word Studies)
Solidarity is related to union, unity, community, fellowship, and partnership.  In Philemon, Paul writes to Philemon, on the basis of the solidarity they share.  It means that they share a working purpose together in something bigger than themselves.  That sharing is life in Christ.

A big take-away from the letter to Philemon is that the kingdom of God is flat.  Although he was a slave, Onesimus is equal, in Christ, to Paul and to Philemon.  The slave, the Apostle, and the businessman are all in an equal partnership, in Christ.

The 'in Christ' part is not just a theory or ethereal, but the living reality.  The person in the kingdom with the most visibility is equal to the new believer.  That one is the new brother or sister and that one is an elder or a mama or papa, in Christ.

In the kingdom, all people have gifts, roles, functions, and offices.  Your gift, role, function, or office. do not make you a boss of others or a superior.  There is no hierarchy in the kingdom.  That is the way non-believers conduct affairs.

If you are a leader, you are in a role where you are functioning in your gift(s).  Some examples are: Sunday school teacher, home fellowship leader, worship leader, outreach leader, mission team leader, and a hundred other examples.  These are all serving roles.  These are all servants, servant leaders.

In the church, we call it servant leadership.  In servant leadership, we invite people to follow, we point the way, and we come along side people and support them.  When the people you are leading need stern control, for their protection or for the protection of others, sternness is called for.  But that is not the norm.

With gift, role, function, and office all standing on the flat plain of solidarity, community, partnership, or fellowship in the kingdom; we also have the issue of authority.  Paul had apostolic authority.  You and I, like Paul, Philemon, and Onesimus; have a measure of authority, in Christ.

Authority comes with gifts, but the authority is always for building people up in Christ.  Paul, the Apostle stands on the flat ground of solidarity that he shares with Philemon and entreats him, as a brother.  This is an amazing example of Christlike conflict resolution, in the church.

Christians are in union with Christ, which makes them in union with other Christians.  Christ is the basis for all relationships in the kingdom, which includes the church.  If you have something against someone, like if you feel or believe they have wronged you, and you are both Christians, then the question is, "how does your mutual union with and solidarity in Christ, come to bear on this conflict?"