Globalism isn't inherent to socialism or capitalism. It can work equally good in either.
It's almost as bad as the people that think Hitler was bad because he was "socialist". As if it had nothing to do with the death camps, because apparently if he wasn't socialist, he would've been a much better person...
I think it all stems from an inherent lack of understanding about what exactly constitutes "socialism" and "capitalism", as if they exist only in one form in practice. Hitler was nothing remotely close to a typical private property, free market capitalist, but neither was he an advocate for a completely state-run economy.
When people talk about "Globalism", it can (and does) take many forms. Even if there were suddenly a singular world government, that would not necessitate that it be socialist or more capitalist-oriented. I suspect people spend more time being afraid of scary words and concepts than actually thinking them through.