Russian Christians are lucky that they have a working alternative service system. Some running into a problem if they were active duty before becoming a Christian, the worst case I heard one was sent to a remote settlement, which is not a prison, but a half-way house style life (driving a car, working at prescribed factory) but with restrictions. When the armed conflict started, and many young people were afraid of a possible draft, the authorities just let these people leave the country. Good number of those who left returned already.
The Ukrainians are in a much worse situation:
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In general, the draft in Ukraine is a total mess. When the armed conflict started, all men from age 18 to 60 were prohibited to leave Ukraine. Only handicapped men and fathers of 3 or more children were allowed to leave. That is how most of Christian families managed to leave Ukraine (they generally have a bigger family like Anabaptist folks in the US). But if you have only 2 or fewer children, you are out of luck in Ukraine.
Men of draft age (from 27 to 50, average age of a solder is 43) are being hunted on the streets by Ukrainian police and military draft office. There are tons of video of that manhunt. Very brutal. The medical fitness test is abused by the military authorities, and handicapped and mentally ill men are being drafted and sent to the battle lines. There were videos of such men being captured, which shocked even the opposite side, because they are obviously unfit for any service.
Many men (not only young) illegally cross the border to Moldova, Romania, Slovakia, Poland, Hungary and even Belarus and Russia to avoid the draft. They hike through the mountains, dirt biking through using the trails, kayaking, swim across the rivers, scuba dive, use skiffs on the sea, cross country skiing etc. There are a number of YouTube channels where they share their stories and give advice on how to prepare and where to cross. There is a joke that Mr. Zelenskyy is the best promoter of extreme tourism. Unfortunately, some of the fugitives died while crossing, some were killed, some were captured by the border guard.
The Ukrainian border is the best protected border in the western hemisphere. They use helicopters, drones, thermal vision cameras, etc. EU provide equipment to guard it better from the draft dodgers:
Those who managed to escape so far were granted protection by the neighbouring states, but they generally move to the countries away from Ukraine border (like Norway, Spain, Germany, even North America) to make it harder being returned in the future if the situation change. My son knows personally a Christian young fellow who fled Ukraine that way.
