Earlier quoted context omitted.
If I was the CEO of Pepsi and saw my employee tweet how he likes Coke I would be pissed. Morality is subjective so nobody can say what's truly "right" or "wrong", but it is true that what this guy did was not a cool thing to do. And I can imagine just reading through his post what other things he probably may have done to result in him getting fired.
Ahh so if you work for Dodge you can only buy a dodge?
It's not a requirement, but it hints at not believing in the company you work for. Imagine the drama if Uber's CEO preferred to use Lyft.
If you don't have confidence in the product, it implies that you are just there to collect a paycheck. The optics from an outsider is that you have no confidence in Gitlab and the work that you do. It looks especially bad considering Github is your direct competitor. Its like a member of the LA Lakers wearing a Boston Celtics jersey to warmups