Is a Christian allowed to solicit funds from a congregation which his home congregation has no fellowship with for evangelistic works? For example, one from a conservative church and the other a liberal church.
Sending funds to support the preaching of the Gospel is a form of fellowship, or sharing. It shows that the giver and the receiver both agree. "Now you Philippians know also that in the beginning of the gospel, when I departed from Macedonia, no church shared with me concerning giving and receiving but you only. For even in Thessalonica you sent aid once and again for my necessities" (Philippians 4:15-16).
But when there is disagreement in doctrine, there cannot truly be a fellowship. "Whoever transgresses and does not abide in the doctrine of Christ does not have God. He who abides in the doctrine of Christ has both the Father and the Son. If anyone comes to you and does not bring this doctrine, do not receive him into your house nor greet him; for he who greets him shares in his evil deeds" (II John 9-11). A congregation supporting someone they think is teaching false doctrine isn't sensible.