In the 60's the left was always politically closer to Russia, now it seems the right (Trump, LePenn, etc) are more pro Russia. Why?
Because Russia in the 60s was a different country than Russia in the 21st century.
In the 60s, Russia was called the Soviet Union and was the leader of the Communist world. Communism is generally considered a left political movement.
But that doesn't mean that all political left are/were communist. And even those which self-identified as communist didn't all necessarily agree with the very authoritarian Stalinist interpretation of Communism as practiced by the USSR.
But then why the impression that the political left in the 60s were close to Russia? Back in the cold war, communism in general and the USSR in particular were considered the primary political enemy of the western world. So denouncing political enemies as communist supporters was a common propaganda tactic (compare McCarthyism). Dismissing a whole political direction as "communist traitors" due to a few of them being open USSR sympathizers was a convenient way to delegitimize them.
But today's Russia isn't the Soviet Union anymore. After the fall of the Soviet Union, Russia became the Russian Federation and made very radical political changes. The Soviet planned economy was reformed to a capitalist free market economy. So there is nothing left which an ideological communist might idolize Russia for. But on the other hand, modern Russia implements some political positions which are generally associated with the political right, like anti-LGBT, promotion of traditional family roles, etc.
There are two axis here:
The first one is ideological, in the 60s the Soviet Union was a Communist state and for most of the left it was, if not a model to follow, a counterweight to the capitalist system and a sign that capitalism was not the only possible system.
After the dissolution of the Soviet Union, Russia under Putin has become extremely nationalist, expansionist, culturally backwards (e.g. their treatment of homosexuality) and capitalist, and shows little regard for laws human rights when these oppose any of the above. This appeals to part1 of the right wing public.
The second one is geopolitical, both the SU of the 60s and current Russia are competing for areas of influence. In the 60s it meant that leftist leaning regimes were likely to receive Russian help, specially if those regimes were under pressure from the USA. That kind of support helped to improve the SU standing between left leaning people and worsen it between right leaning people.
In that axis, nowadays there are still many right wing people in the USA and Western Europe that dislike Russia as a competitor, even if ideologically it is closer that it was before.
TL/DR; Many right wing people still does not like Russia, but some of those who previously were opposed due to ideological differences have changed their stance. There is less opposition to Russia, but it still exists. Adding to that, the left now shows a lot less of support to Russia which makes right wing examples more notorious.
1Let me insist that I only talk about part of the right wing public. Political opinions are very diverse and there may be people who consider themselves right leaning but may ideologically dislike Russia policies as too extreme.
First and foremost, because the Soviet Union is not Russia. USSR was officially dissolved through a legal proclamation on December 26th, 1991. That's 25 years ago. It had existed for 73 years. Those are just facts.
A more detailed and clear picture comes out of how and why USSR was dissolved. Most would point to an economic collapse after its inability to economically handle the Chernobyl fiasco. But that doesn't quite cut it. Roughly at the same time as Soviet Union was introducing a mixed economy, China was doing the same thing. And China did not have any seismic economic event which would precipitate the switch. Fully socialist economy (with full government ownership of all the means of production) turned out not to be economically tenable in China just as it did in the USSR.
And while the reforms in China were led by the government, the Soviet Union experienced a period of social unrest which led to the collapse of the government. In other words, the modern Russian state emerged out of a rebellion against the Soviet Union. And since the USSR was the embodiment of the Left's tenants, it was natural for the Left to support it while it existed.
The Right in the US is not a big fan of the modern Russian state because, starting around 2006, it swerved off the path towards a liberal democracy (with a capitalist economic system) towards a nationalist mixed-economy in which business has the 1st word in solving economic problems while the government has the last word in everything. And, as all nationalist states, it remilitarized and started looking for enemies to justify its existence. The US Left views the modern Russia as an ideological enemy. It did, after all, rebel against the USSR.
The Russian Federation's view on the West is mixed. On the one hand, it still views itself as the state born out of the rebellion against the USSR. So it expresses much stronger affinity towards right-leaning parties abroad. On the other hand, as a nationalist state, it is looking for enemies to fight and the West (as a traditional enemy) presents itself as one of possible targets for enmity (even if not for outright aggression).
It's easy to see why the confusion you express exists. Because the collapse of the USSR is often attributed to US Right's (and Reagan's, in particular) efforts to force USSR into another arms race on SDI. So the simplistic conclusion to draw is that Reagan was an enemy of Russia for xenophobic or cultural reasons.
But that was demonstrably not the case. Reagan's view on Russian people was that they were victims of the Russian leftist state because he viewed leftist ideology as inherently damaging to human condition. He viewed the opposition to the USSR as a humanitarian effort. There is a large body of statements that he made which support this view. From the fact that he was fond of Russian folklore to the fact that he thought that he would be able to convince the Soviet Premier to change the Russian economic system simply by demonstrating that consumerism brought about a better quality of life in the US than the Soviet economic system brought about in the USSR. He clearly thought to actually improve the quality of life both at home and abroad with his attempts to change the ways of the Soviet Union.
Now that the USSR is slowly vanishing into the memory of history, it is only natural for the right to not see in Russia the ideological enemy which Reagan saw in it. Again, it is the state born out of a rebellion against the USSR. But you won't hear too many calls on the Right to embrace Russia as a close friend because the Right does take national defense priorities more vigorously (regardless of whether that's warranted or not). And it is fully aware of the fact that the new Russia's need for enemies may make the West a target.
It is difficult to tell who is right and who is left in the USA. I would divide the US spectrum into "globalists" and "anti-globalists".
Globalists were always against the USSR. They support expansion of NATO, the EU, international trade treaties, copyright enforcement, bombings and color revolutions in other countries, free trade, refugees, feminism, restriction on alcohol while legalizing the drugs, anti-Catholicism, rising age of sexual consent, pedo-hysteria, restriction of teen rights, state intervention in family, LGBT rights, affirmative action, islamism internationally.
Anti-globalists support non-interventionism, protectionism, leaving international trade treaties and military alliances (while supporting disarmament treaties), restriction of immigration, less support for NATO and EU, free software, space exploration, more support for Israel.
Typical representatives of globalists were Carter, Clinton, Obama. Typical representatives of anti-Globalists were Ford, Trump. Others were in middle.
I think the Americans often call globalists "the left" while anti-globalists "the right" but they are both right on international scale.