Kind of telling on themselves here, right? If "everyone is welcome" is an "ideology", kinda indicates the person labeling as such is against it. I say this because the societal norms on paper for every major philosophy or ideology would be in favor of that idea, and if it strikes you as staking a claim to something new, it probably took some mental effort to get to that conclusion. Would "be kind" be ideology? Technically yes I guess it is, but I doubt these people would be pissed about it and call it out like this. Are they asking for those cat posters saying "hang in there" to be taken down? That's preaching the "ideology" of persistence.
The Italians, and to a lesser extent the Irish, are mostly Catholic, which doesn't really count a Christian, and therefore they don't actually count as white.