If people avoided visiting countries because of illegal invasions, the UK, US and some others would be quite short of visitors. Let's not even get into countries with massive human rights abuses that we are happy to visit and trade with. But people are people and I believe it's wrong to judge the people of a country by its government. Travel is best undertaken with an open mind, if that bothers people, don't travel. But please don't preach at others where they should or shouldn't go on political grounds. This is not the forum for it.

In response to your question, yes, such a journey is perfectly possible.

Today's possible routes east inevitably go through Russia to a greater or lesser degree. Going through places like China and some of the SEA states is a right headache. Crossing points from Europe into Russia are open, and Russian embassies are issuing tourist visas. If you use a visa agency it's easier. Baltic crossing points are reputedly on a go-slow, taking 3-4 days to let people through and confiscating any Euros they find. The best way is probably via Turkey and Georgia. Quite a few people have done that and it works fine. From there you can either head north to the Trans Siberian Highway (which is very long and a bit boring) or go round the Caspian to Kazakhstan and Uzbekistan, which will take you down into the Central Asian states. After those, head north from Almaty which will take you up into Siberia and the road to the east is yours.

From all reports, people who go to Russia as guests are treated as guests. Your biggest problem is likely to be that western cards don't work there, so you'll need to arrange to get sufficient cash before entering the country. You will be able to change USD to RUB easily, EUR maybe not quite as common but certainly possible. Look into opening a Tinkoff debit card account for foreigners if you're expecting to be in Russia for some time and don't want to carry large amounts of cash. You should be able to buy road and health insurance locally from somewhere like Rosgosstrakh.

It's a great trip and will present plenty of challenges. Hope you get to do it.