You're entitled to your own opinion - Not to your own facts

So, tomorrow there's this lefties conference at one of the Student Unions. Exciting! I've talked myself into going with the intention of keeping quiet and listening carefully to all the arguments and positions I will encounter. How thoughtful of me, not to ruin their conference with unconventional views!

Anyway, as a pre-runner, I'm doing some reasoning regarding freedom of opinion - your right to think whatever you want. Fundamental pillar upon which our western democracies rest. Let's go.

One of the most interesting clashes of politics is facts vs. opinion. We all, predominantly, recognize that other people are entitled to their views, just as I am entitled to mine. However, what happens when such opinions are countered with plain facts, insofar that such facts can be obtained?

First, fundamental difference:
Opinion: I like Ice-Cream
Fact: Ice-Cream contains cream (unless it's vegan, made differently, lala).

Regardless of my opinion about what Ice-Cream contains, or my right to excercise that opinion, it doesn't change the fact that cream is a component of Ice-Cream - thus, it renders my opinion ridiculous, superfluous and straight out silly.

So, what happens when opinions are based on or fully rely on facts? That is, what happens when the relation between the two are established?

Let me give you an example. Consider a fairly easy statement, "Cats are the best animals!"
An opinion, easy enough, and a very subjective statement. How is "best" to be defined, or even measured? We can't do anything about it, and the freedom of opinion applies fully.

If we add the next layer: "Cats are the best animals, because they have most legs!"
Now we've established a relation to measurable fact, and the person has also implied the indicator for how "best" is to be measured: the amount of legs.

But here facts come in: There are a number of other animals with more legs than cats, say spiders or ants. Applying the person's own measure for why cats are the best animals (namely amount of legs), his/her opinion is invalidated. Cats simply are not the best animals, regardless of this person's view or opinion. He or she is wrong. Not from my point of view, but from any point of view.

How is all of this relevant for a Leftie Conference?

I tend to encounter socialists or people on the left that carry certain ideas and believes that I find preposterous. Fair enough, we're all entitled to opinions, which is a major criticism I get when I say they're wrong or should change their views: "We're all entitled to our own opinions, why don't you let me have mine?"

Well, insofar as
1) an indicator for measuring that opinion is provided,
2) facts for that indicator can be obtained, and
3) there's a straight relationship between the indicator and the opinion, i.e you use that indicator to say why exactly your opinion is prefered,
then your opinion can be made as useless and incorrect as the one about cats above.

That is, if I can prove to you, within these three conditions, that your ideology is incorrect, your statements invalid and your facts wrong - then no, you're no longer entitled to have that opinion.

This is, I think, essentially why I wanna go tomorrow. If I can prove to lefties that their perception or ideas are factually incorrect, they are obliged to change their position, those perceptions and ultimately their entire ideology.

Seems easy enough, why do we still have socialists around?