Yes. Salesforce is used in a browser and Salesforce supports Chrome, Firefox, Edge and Safari, so a Linux machine running Chrome or Firefox works normally.
Salesforce by Salesforce, Inc. · Business & accounting · Works in a browser
Salesforce has no desktop program on any operating system. Everything happens in Lightning
Experience in a browser, and Salesforce's supported browsers page lists the latest stable versions
of Google Chrome, Mozilla Firefox, Microsoft Edge Chromium and Apple Safari. Chrome, Firefox and
Edge all have Linux versions, so nothing about your daily work changes.
There is no data to move. Your records live on Salesforce's servers and you simply sign in from the
new machine. This is one of the few business products where switching operating system is a
non-event.
Two details from Salesforce's own documentation are worth knowing. Lightning Experience does not
support private or incognito browsing windows, so use an ordinary window. And on tablets only iPad
Safari is supported, with the Salesforce mobile app recommended elsewhere, which is unchanged from
how it behaved on Windows.
The thing to check is anything bolted on around Salesforce. Outlook and Word integrations, desktop
dialers, and some partner tools are Windows programs rather than part of Salesforce. Make a list of
those before you switch, because each one needs its own answer.
Only relevant if you want to leave Salesforce rather than keep using it. Browser-based CRM with a free single-app plan, far simpler and far cheaper, and correspondingly less capable.
Your files: No Salesforce file format to worry about. Contacts, accounts and opportunities move as CSV exports.