In that day, leaven was the portion of old, fermented dough needed to make a new loaf of bread rise before baking, with the word leaven expanded to illustrate anything that envalues a transaction.
So the Son-of-God Joshua's warning was against anyone conceding their trust in God to anyone else's organization, or of letting anyone manage their faith in return for goods, services or status, lest that faith be compromised.
Tradecraft against compromise is generally ignored by the American Christian church, which is itself compromised by the famous 501(c)(3) educational tax exemption, that registers applicants as private social clubs, i.e. little government offshoots, despite insistence of church-and-state separation.
Plus it is a compromiser because anyone broaching the ‘beware the leaven’ subject is told that the verse anachronistically warns against believing the lies of rival denominations, and because many churches offer salaried positions to teach their partisan religious materials, in return for a cut of monies collected -- marking pastors as employees working for franchised systems, and not for God.
Who remembers Shadrach, Meshach and Abednego? These three bondsmen refused to bow down to a great gilt statue of Nebuchadnezzar II, who, although he liked them, was obliged under Hammurabi Code to execute them in the fiery furnace.
Once thrown in, they not only didn't die as expected but were seen walking around in the flames with a fourth person suspected at the least to be an angel-of-God, and at the most, the Chief Archangel later known as the-Son-of-God.
In his time, the Son-of-God was taunted for not being a product of Pharisaic schools. That opinion—today our law of copyright—commanded that if any teach about God it was to be the official version of God, by people registered by said officials, so they'd get a cut of any proceeds. Ultimately aware that the Son-of-God would not be compromised to their marketing—he not giving an inch—they had him killed under the treason act.
Only thankfully he didn't stay killed but resurrected just to show 'em. And it is to his resurrection in which we trust, not to any government concession.