Autocompletion doesn't work when using ALE + deoplete

Question

From my init.vim (I've checked that it doesn't work even with a minimal configuration):

call plug#begin()
Plug 'Shougo/deoplete.nvim', { 'do': ':UpdateRemotePlugins' }
Plug 'dense-analysis/ale'
Plug 'lervag/vimtex'
call plug#end()

let g:deoplete#enable_at_startup = 1
let g:ale_cpp_ccls_init_options = {
\   'cache': {
\       'directory': '/tmp/ccls/cache'
\   }
\ }

call deoplete#custom#var('omni', 'input_patterns', {
      \ 'tex': g:vimtex#re#deoplete
\})

When I open a .cpp file, sign column shows up and error/warning messages are displayed as expected. However, there are no language-specific autocompletion suggestions (i.e. the ones that should be provided by ALE/ccls; there are only snippets and basic suggestions like variable names).

Everything works fine with .tex files. It also works if I use LanguageClient-neovim (also with ccls) instead of ALE.