Praise be to Allah.
You have done well by stipulating that nothing should be included that goes against Islamic sharee’ah. If you state some examples, such as music, pictures of women and songs, that will be better, because some of those who use the internet may be unaware that these things go against sharee’ah.
Whether you stipulate these conditions or not, it is not permissible for those who sign up with you to put anything haraam on their sites, for disobedience to Allaah is something that must be avoided, and that does not depend on conditions stipulated by anyone. The Prophet (peace and blessings of Allaah be upon him) said: “Whatever I have forbidden to you, avoid it.” Narrated by al-Bukhaari, 7288; Muslim, 1337.
It is not permissible for you to approve of anything that is haraam, or to help the one who wants to put it on his site, for Allaah has forbidden that when He said (interpretation of the meaning):
“but do not help one another in sin and transgression”
The condition that has been stipulated is simply to reinforce this message and make it clearer.
Based on this, if someone puts something haraam on his site, you have to advise him and ask him to remove these files. If he responds, all well and good, otherwise you have the right to remove them and not renew his contract.
Do not worry about your reputation; it is sufficient to please Allaah and be accepted by Him.
Al-Tirmidhi (2414) narrated that ‘Aa’ishah (may Allaah be pleased with her) said: I heard the Messenger of Allaah (peace and blessings of Allaah be upon him) say: “Whoever seeks to please Allaah by displeasing the people, Allaah will suffice him and protect him from the people. But whoever seeks to please the people by displeasing Allaah, Allaah will leave him to the people.” Classed as saheeh by al-Albaani in Saheeh al-Tirmidhi.
In His hands are the treasures of the heavens and the earth,
“And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty).
3. And He will provide him from (sources) he never could imagine”
A little that is blessed is better than a great deal in which there is no blessing.
And Allaah knows best.