Should all pursue entire sanctification?
Yes. It should be sought earnestly by every child of God.
Catechism for the Global Methodist Church, question 73
2Speak to all the congregation of the sons of Israel and say to them: You shall be holy, for I the LORD your God am holy.
11Teach me your way, O LORD; I will walk in your truth. Unite my heart to fear your name.
14Pursue peace with all and the holiness without which no one will see the Lord.
13Therefore, having girded up the loins of your mind, being completely sober, set your hope upon the grace that is being brought to you at the revelation of Jesus Christ. 14As children of obedience, do not be conformed to the desires that once governed you in your ignorance, 15but, as the one who called you is holy, become holy yourselves in all your conduct. 16For it is written, 'You shall be holy, because I am holy.'
3As his divine power has granted to us all things that pertain to life and piety through the knowledge of the one who called us by his own glory and virtue. 4Through which the precious and very great promises have been granted to us, so that through them you may become participants in the divine nature, having escaped the corruption that is in the world by desire. 5And for this very reason, after supplying all diligence, supply virtue in your faith, and in virtue supply knowledge. 6And in knowledge supply self-control, and in self-control supply perseverance, and in perseverance supply piety. 7And in piety supply brotherly love, and in brotherly love supply love. 8For when these things are yours and are increasing, they keep you from being idle or unfruitful toward the knowledge of our Lord Jesus Christ. 9For to whomever these things are not present, he is blind, being nearsighted, having taken forgetfulness of the cleansing of his former sins. 10Therefore, brothers, be more eager to make your calling and election firm; for by doing these things you will never stumble. 11For in this way entrance into the eternal kingdom of our Lord and Savior Jesus Christ will be richly supplied to you.
The catechism now asks who entire sanctification is for. The answer comes from the same sentence of Article XI of the Confession of Faith that the previous question used: this gracious gift "should be sought earnestly by every child of God." ΒΆ102.6 of the Book of Doctrines and Discipline says the same in the church's own voice: a life of holiness, and in the end entire sanctification, "should be the goal of each person's journey with God." Christian perfection is therefore a doctrine for the whole membership rather than for a spiritual elite.
Every child of God answers the question of scope. The command to be holy was given to "all the congregation of the sons of Israel" (Leviticus 19:2), and Peter applies it to every Christian without exception: "as the one who called you is holy, become holy yourselves in all your conduct. For it is written, 'You shall be holy, because I am holy'" (1 Peter 1:15-16). Hebrews frames the pursuit of holiness as a condition of seeing the Lord at all, "Pursue peace with all and the holiness without which no one will see the Lord" (Hebrews 12:14), which leaves no believer free to consider it someone else's business.
Sought earnestly answers the question of manner. Second Peter describes what earnest seeking looks like. God's "divine power has granted to us all things that pertain to life and piety," and through his promises believers "may become participants in the divine nature" (2 Peter 1:3-4). The gift comes first; then the effort. "For this very reason, after supplying all diligence, supply virtue in your faith," and so on through knowledge, self-control, perseverance, piety, brotherly love, and love itself (2 Peter 1:5-7). Those who do this "will never stumble" (2 Peter 1:10). The psalmist's prayer shows the inward side of the same seeking: "Teach me your way, O LORD; I will walk in your truth. Unite my heart to fear your name" (Psalm 86:11). A united heart, undivided in its love, is what entire sanctification names.
For a Methodist this teaching turns a doctrine into a prayer. Wesley expected his people to ask God for perfect love, to expect it, and to keep asking until they received it, using the means of grace all the while. The catechism does not say that every believer has obtained it; it says every believer should seek it, and Article XI promises that every regenerate believer may obtain it.