Yeah but that could stop any chance of their potential conversion or me being at a good influence on them.
Not saying this is you, but this is the typical excuse that trad families use to keep ties with relatives who dress immodestly, etc.. Sometimes (rarely) that might be legit, but what it most often is, is human respect weakness - the expectation of which is they will corrupt you, not the other way around.
In reality, when they know why you have disowned or can have nothing to do with them, *that* is your good influence, *that* is their incentive for conversion - meanwhile you have freed yourself (and those in your care) of any bad influence etc. from their company.