Heya stockfish. I’ve been using battle dot net through lutris on Heroes of the Storm, Hearthstone, Overwatch, and World of Warcraft, with no issues or warnings from blizzard.
As for your crashing issue, pull up your lutris launcher, right click Hearthstone and click “wine configuration”. on one of the tabs there should be a dropdown menu labeled “windows version”. Click that, and try setting it to Windows 10, and then try.
Also, typically dropping a question unrelated to the thread is bad etiquette for message boards; it makes it harder for others who have the same issue to find the proper solution. A good place to look for solutions to any issue is to check the game’s page on lutris, and comb through the replies to the script to see if anyone has solved it already. If not, create a new thread with the issue or a comment on the game’s page.
Let me know if this works for you, and if not we’ll dig a bit deeper!