Authoritarian type parties on the hard-left and hard-right may not represent the furthest ends of the political spectrum but still mirror each other in significant ways.
Take the anti-pragmatic side of the United States Republican Party (especially the Religious Right) and compare it to the modern Communist Party of the Russian Federation and you can find quite a few similarities (besides the obvious one that both are ideologues focused on the "purity" of their movement), especially on social policies. In fact, if each party's leaders avoided talking to each other about economics they would find more common ground than they may expect, especially considering their vehement hatred for each other. For instance:
Both strongly endorse "tough on crime" policies and the death penalty.[1]
Both strongly support "traditional values," meaning hardcore social conservatism, pro-life attitudes.[2] and hostility to LGBT rights.
Both have weaknesses for conspiracy theories, especially the conspiracy theory that there is some deliberate effort to destroy morality.[3][4]
Both are fervently patriotic and support some form of nationalism while holding the belief that each of their countries are the greatest in the world. This leads to some supporting a degree of historical revisionism as well.[5][6][7]
Both are reactionary in nature and extremely nostalgic for some sort of "golden age" (Stalin for the commies,[8] Ronald Reagan or the 50's[9][10] for the GOP).
Both support increasing spending on an even larger national defense while rarely questioning if it's necessary. Also, they both tend to admire "masculinity" and militarism.
Both have a weakness for "boogeymen," with liberals being a common target for both parties.
Both make populist appeals to the lower classes, mainly by promising to cut their taxes,[11] regardless of whether it will be done or whether it can be afforded.
Both have a love of dramatic rhetoric, even by political standards.
Both support largely discredited economic crankery that is usually defended with "common sense" type arguments.
Both have strands of anti-intellectualism, with intellectuals who question them being seen as "elitist."
Both are currently trying to appeal to the religious majority in each of their respective countries, with even CPRF leader Zyuganov citing the "spiritual values" of communism in his speeches to appeal to followers of the Russian Orthodox Church, despite the party being historically atheist.[12]
Both support censorship, and passing legislation to stop the "degradation" of national symbols.[13]
Both, hilariously, blame each other for the supposed "degradation" of art, literature, culture, and philosophy. The commies claim that the embrace of capitalism has left these areas bland because artists are only concerned about profit, not quality,[14] whereas the Republicans like to say that "leftists" or "secularists" have ruined these areas because their "hostility" to religion has harmed creativity.
Both like to reference revolutionary heroes from their nation's past in their arguments,[15] usually by claiming that they are fighting for the same values they were, which is commonly followed up by saying that what they stand for is "True American/Russian values," whereas their opponents stand for evil/radicalism. They may also liken themselves to being the "underdogs" in their current fight, like said revolutionary leaders. Expect these historical figures to be glorified and their flaws to be ignored/excused/downplayed.[16][17]