You're talking about a highly specific case where the ist/ic is a response to a provable fact presented without implications or conclusions. For example, "Black Americans commit crimes at a disproportionately high rate," spoken in a vacuum.
If so, fine. I agree with you. A provable fact can not in and of itself be a racist statement. A writer can disregard ist/ic criticisms to this effect.
But how often do our statements regarding race fall into this narrow category? One in ten times? One in a hundred?
For starters, such statements are usually made in the context of a contentious social or moral issue (e.g. "Does white privilege exist?", "Should black ghettos be gentrified?", etc.) and broad statements about race at the very least strongly imply the writer is invoking them as justification for his position. The statements "Black Americans commit crimes at a disproportionately high rate. ...ergo the persecution they claim is systemic is in fact self-inflicted." or "Black Americans commit crimes at a disproportionately high rate. ...ergo gentrification of black ghettos is less objectionable than gentrification of ghettos generally." with the added implications are no longer provable facts. The former becomes an unproven (and indeed, highly controversial) assertion, and the latter becomes a judgment based on morals and principles that not everybody shares.
My point being that even provable fact (what you call a "true claim") is rarely made in a vacuum, and any given ist/ic slinger may not be attacking the statement itself but instead what he feels is reasonably implied by the statement in the context of the discussion. His intuition about the implications may or may not be valid, and his slinging ists/ics at these implications may or may not be valid. It needs to be judged on a case by case basis.
This is just the case where the fact is provable and presented without conclusions--extremely rare circumstances, in my experience. Far more often there's some degree of uncertainty, subjectivity, or moral judgment involved. Any time these elements come into play, ists/ics can reasonably apply (that is, we can't summarily dismiss the criticism as inapplicable). We have to try to understand what the critic is saying, what he thinks we're saying, and deal with it on that basis, as I said in my previous post.
If I'm coming across as though I'm in complete opposition to the OP, I'm not. I generally agree with you that the ists/ics have been overused to the point where they're nigh meaningless in online discussion. However, your argument that they "are not rational arguments, they are slurs designed to make people be quiet" is overgeneralizing. It's not universally true, and we can't take this for granted. We have to look at the critic and the context, figure out what's being said and perceived, and generally do our best to take others seriously.