If a plugin is available for Moodle 3.7 but not for 3.8, it does not necessarily mean that it is incompatible. Very often, it just means that the author just did not have time to check it for compatibility yet.
Before you install it though, read the comments on the plugin page and in the plugin's bug tracker. If there is a link to the a discussion, check there too. Very often you will find comments from people saying that they tried it and it works in recent versions of Moodle - or they will mention what did not work. You may be willing to live with an issue that doesn't affect you (e.g. feature you don't use).
The other thing to check is the Versions tab on the plugin page. I noticed that many authors may not configure the settings for their plugin page correctly. As a result, the version compatibility listed at the top of the plugin page is outdated. Checking the Versions tab, you may discover that the latest version of the plugin is actually compatible with your installation of Moodle.
Another thing you could do is to drop the author a message indicating that you would like to use it on Moodle 3.8. Sometimes, when I do this, a new compatible version pops up shortly afterwards. Plugin authors love to know that people are using their plugin and find it useful. Your request might just be what is needed to motivate the author into releasing an updated version.
I did a quick check for you. The bad news is that there is no indication anywhere that the moodle-enrol_attributes plugin is compatible with Moodle 3
8. The good news is that nobody has indicated that they've experienced any issues with the plugin in 3.8 either.
If I were you, I would give it a try. Unless you have the ability to fix a problem if things stop working, I recommend that you try it first on a different Moodle site, perhaps a local copy of Moodle on your computer. If it works on your computer, great! It will very likely work on your live Moodle site too. Post a message on the plugin page to let others know if it is compatible or not.
Almost forgot. One more place you can check is the source code repository on Github. If you see some recent updates, it is a good sign that the author is updating the plugin and that a new version is forthcoming.
At this point, I suspect that many plugin authors are busy preparing and testing their plugins for compatibility with Moodle 3.9 due next month. I know I am with my plugins.
Hope you find something useful in all of this.