Homosexual couples are not allowed to adopt children. In most of Europe for that matter, I think. Though I don't keep up with the statistics, I may be wrong.
Well, mostly it doesn't even have to do much with religion or being eastern, it's just that due to being practically another world due to socialist rule, Eastern Europe and by extension other countries of the socialist block never went through the sexual revolution and growth of tolerance as the western society did.
There is actually a reversing process in a lot of former socialist states, because during those times tolerance of other nations and races was government-forced and homosexuality was forbidden with punishments for sodomy being up to 10 years in prison.
After the collapse of socialism, nationalism and radicalism grew incredibly quickly, with all the following consequences. The sheltered post-socialist societies were mostly not ready for the sudden liberalisation and introduction to the modern Western society. As a result, Western culture and economy has flooded the former socialist block, bringing with it a rise in crimes and countries falling into extreme poverty.
It's been years since then, but the catastrophic results of those events are present even now, with homosexuality and Western liberalism being seen by many as corruption.
It's no wonder, considering that the people were introduced to the liberal and capitalistic society that they dreamt of joining for so long, as their countries collapsed into chaos, crime and poverty.