Personally, my biggest concern is data continuity. I suspect whatever measures the company took previously to ensure data continuity are still in place. However, to be on the safe side I backed up my journal + comments using the following version of LJArchive: http://www.memory-prime.de/lja/ljarchive_setup.zip. I should note that anyone who chooses to use this should back up the installer as well, otherwise the .lja file would not be all that useful.
Although honestly, I think I should be more skeptical of installing a random piece of software on my system and providing my LJ credentials to it than to use an otherwise trusted service on Russian servers. I felt somewhat reassured that I found it via a comment from a known good LiveJournaler, xtingu.
Another alternative is Dreamwidth, which uses the same engine, allows you to import your LiveJournal, and apparently allows pretty seamless cross-posting. There was an exodus (or perhaps multiple exoduses) to Dreamwidth in years past. I am considering that as well.
After data continuity, my other concern is censorship. Although I am unlikely to be censored by LiveJournal as I am politically insignificant, more influential Russian LiveJournal users might be censored if they speak out against, for example, Chechen concentration camps.
In spite of my political insignificance, I will say that the camps are horrific, and Russia is allowing this to happen in the quasi-independent state of Chechnya. So go ahead, censor me Russia. The point is, why share a platform that supports censorship? Not that I have any evidence of censorship at this time but that's clearly what we all anticipate.
My third concern is security/privacy. This may be more of a concern for other users, but as open as I am here, I have paper-based journals for other material. LiveJournal has made some questionable technical changes. In an era where some are advocating for HTTPS everywhere, the site now defaults to HTTP. The session cookies are not secure, so users are vulnerable to session hijacking, particularly via session-sniffing. (The session cookies do use httpOnly and so are not as vulnerable to cross-site scripting.) I wouldn't log into the site from an untrusted network, and remember that your friends-only posts are only as secure if all your friends' accounts are secure.
The LJ user formerly known as boutell has been running the social blogging site One Post Wonder for years now. It's a good alternative to LiveJournal, although you won't be able to import your LJ entries and comments. I have 45 invites, in case anyone would like to try it out. I'm there too, even more quiet than I am here.