Okay so did you even read that? Your own link says it is a feature of “popular discourse” - ie not supported by actual evidence - and then says:

Several political scientists, psychologists, and sociologists have criticized the horseshoe theory. Proponents point to a number of perceived similarities between extremes and allege that both tend to support authoritarianism or totalitarianism; political scientists do not appear to support this notion, and instances of peer-reviewed research on the subject are scarce. Existing studies and comprehensive reviews often find only limited support and only under certain conditions; they generally contradict the theory’s central premises.

That’s about as close as an impartially worded style of article can come to saying “yeah this is obviously bullshit”.