Redmine

It depends on your shared hosting :)

Upon close investigation of mine. I found out that, while many shared hosting companies offer Ruby and Rails environments, you still need to find out in advance about, how many forked processes will your shared hosting allow you to run in your Ruby app environment. They tend to have harsh limits!
Perhaps the recent version of bundler became a real forkbomb, so you will probably need to gem install bundler -v '1.11.2' which the one of the latest versions of bundler that wasn't fork hungry. Else you risk in failed installation of bundler itself, because you will run out of user processes.
No bundler = no quick way to install all the gems Redmine requires to run.

Then you will need to find out if whatever OS your shared hosting is running does have the required development libs preinstalled for the following gems:

• nokagiri
• mysql2
• redcarpet

Which Redmine also needs, else you most likely wont be able to install and build one of these gems or even all of them.

P.S. Yes, Redmine really needs shared hosting optimization. IMHO it's literally sad that a tool for productivity, really forces it's users into VPS option, since, figuring out whether your Shared hosting is compatible with Redmine will most likely be a waste of time. Unless they thmeselves claim they have Redmine support and many that do, are not cheap at all, especially if you d be just a student who tries to use Redmine for college projects.

It's totally undestrandable that many also would just like to go with cPanel and don't want to waste time to preinstall everything on a VPS and besides, Command Line Interface is so 1980s now, and it's really is time consuming to memorize and tediously type the commands for users who just want to finally use the app avoiding the bash language mess XD
Sadly there aren't many choices of Shared Hostings which would be compatible with Redmine, besides many simply just don't care about Redmine anyway, it's not that of a popular software anymore and there are already superior alternatives to Redmine out there today which can perfectly run on a Shared host :)

End Motto: "A truly good software should never kill the first impression" XD

I find that the best way to manually install Redmine is to use Docker container hosting.

Here is the official image: https://hub.docker.com/_/redmine which can be easily deployed on any popular hosting such as AWS, MS Azur, Google Cloud or Digital Ocean.

Shared hosting is no longer relevant in 2023. Anyway, here are some hostings with Ruby on Rails:

• Liquid Web
• Hostinger
• DreamHost
• Bluehost
• HostGator

However, I would recommend using Redmine dedicated hosting with maintanance and support, such as RedmineUP Cloud