Solution
Add pushurl to remote branches in .git/config:
.git/config
[branch "master"]
remote = github
merge = refs/heads/master
[remote "github"]
fetch = +refs/heads/*:refs/remotes/github/*
url = git@github.com:$user/$project.git
pushurl = git@github.com:$user/$project.git
pushurl = git@gitlab.com:$user/$project.git
pushurl = git@bitbucket.org:$user/$project.git
[remote "gitlab"]
fetch = +refs/heads/*:refs/remotes/gitlab/*
url = git@gitlab.com:$user/$project.git
pushurl = git@github.com:$user/$project.git
pushurl = git@gitlab.com:$user/$project.git
pushurl = git@bitbucket.org:$user/$project.git
[remote "bitbucket"]
fetch = +refs/heads/*:refs/remotes/bitbucket/*
url = git@bitbucket.org:$user/$project.git
pushurl = git@github.com:$user/$project.git
pushurl = git@gitlab.com:$user/$project.git
pushurl = git@bitbucket.org:$user/$project.gitChange $user and $project accordinly.