Trying to keep this as short as possible... In a VM, to test a problem of someone else, I installed a fresh Linux Mint 17.3 and opened Firefox. The search bar (right of the address bar) didn't include Google as an option, as I'm used to. Proceeding to the option to add search providers, I finally found it, along with a "reason" it wasn't there by default.

A little put off by that, but not too worried about it, (they need money too, right?) I found the link for Google and enabled it. Now it was available, and all was good. Except that it wasn't.

Normally, as I type in the search box I get suggestions that lend themselves to what's been typed so far. Often this shortens my typing significantly. Now, it wasn't doing that. I switched back to Yahoo, and it work as normal. Back to Google, no such luck. Not unfamiliar with about:config I poked around, then dug around, and did some comparisons with settings between Yahoo and Google. No dice, can't find what triggers the difference in behavior.

"Ok," says I to self, I'm just go to the repository and drop the Mint custom version, and install the Mozilla original version. Into software manager and drill down to Firefox. No options to upgrade, downgrade, switch versions, or anything else, just "Remove" which, after doing that, only gives the option to "Install." Shows what version will be installed, but no options to change it.

I'm not a Mint user, so I don't know if there's other options for controlling software or not. I'm sure that a source install is likely to be available somehow. But.. Is that the point.

As I understand "Free" software, it's about choice, and not having someone, disto author in this case, dictate what I can use. The option to add Google seemed to fulfill that promise, until I found it only half-worked. Making it difficult, maybe prohibitively so, to replace the restrictive version with an unrestricted version was the icing on the cake.

Edit

So, Linux Mint, Linux kernel and all, is, or is not, Free software? BTW: The source is available, so it's probably "Open source" at least.

The proper question relates only to the version of Firefox, firefox_51.0.1+linuxmint1+rosa, supplied in the repos of Mint, not to the distro itself, or to any other package in the disto, including the kernel. As such, the question should have been, "Does the version of Firefox supplied with Linux Mint 17.3 comply with the MPL and is it still free within the FSF concept?"

Notes:

In re: the "crippling" of the software: I don't know how long I've been using Mozilla products, or Firefox in general, but as their product have evolved, and as I've moved from one distro to another, between OSs, and between platforms, I have become accustomed to features behaving consistently across them all.

I'll not argue, here or in comments, as to whether or not that version is "crippled." I do know that it is modified, and that it does not work the same as every other release of Firefox that I have available to me for testing. The modified source code is available, to anyone who wants it, and according to the accepted answer, modified or not it does comply with the FSF's four freedoms. That was the question, and that is the answer.

I have been replying to comments that go beyond the scope of the question, and I probably shouldn't have been. By my rep, even across SE as a whole, you can see that I'm learning the Stack Exchange way. Comments about the real question will be replied to, while my crippled phrase, my improper scope to include the distro, and related debates won't be fueled by me. Further insights, or explanations that are germane to the OS topic are welcomed and encouraged. That's how others like me can learn.