This is almost correct.
Isn't this like separate lunch counters for blacks and whites during segregation?
No. This case illustrates the difference between discriminating based on sexual preference and making decisions based on your beliefs about marriage. A policy refusing to serve gay people under any circumstances would be discrimination based on sexual preference. That would also be like segregated lunch counters. In this case, however, Arlene's Flowers had no such policy refusing to do business with gay people. In fact, they have employed gay people and had happily and knowingly served gay people for years without any claim of discrimination or hostility. However, this particular event was something they did not want to lend their artistic, professional services to because of their beliefs about what marriage is. You cannot have a policy refusing service to all Mexicans or Japanese people, but you cannot be compelled to do something you don't wish to do simply because the person asking is Mexican or Japanese.
What's wrong with that statement is equating homosexuality with race or ethnicity. Race and ethnicity are not choices. Someday maybe they will be, but right now, they're not. Homosexuality is a choice. It is not genetic very much if at all. It is certainly a choice at least for the vast, vast majority.
It has been elevated to a protected class based upon falsehoods spread about it by its adherents and those who were duped by them.
It is not a benign thing. It is fraught with risks that many have been masking, censoring, downplaying, etc. On the other hand, race and ethnicity are benign. There is nothing inborn in an entire race, nation, tribe, or clan of people making them (all their members) inherently worthy of racial or ethnic discrimination against their members.
Am I advocating for abusing, starving, etc., homosexuals? No, not at all. I am opposed to homosexual marriage and for a whole host of reasons. That said, I do my best not to coerce others. I simply try to say what I say, write what I write, and leave it to those who will hear and read to either grasp, or not, what I've said or written.
Before I leave this subject, let me make clear that I understand that the context of the linked material is the secular law. The secular law within certain jurisdictions, such as the State of Washington, is equating homosexuality with race or ethnicity. I'm not faulting the author of the linked material for that. I agree with the author's statement above provided what else I've written here is understood. I have qualified my agreement.
Let me also add that religious discrimination, per se, is also not genetically based. People do choose to be Christians or not. The reason religion is the first protected class in the US Constitution is a major historical story beyond the scope of this quick post.
Were homosexuality not so inherently dangerous and very often quite harmful, my views would be somewhat different. As I've mentioned before, it is amazing to me that humanity is devolving to the position that males sodomizing each other is viewed as wholesome and to be celebrated rather than roundly condemned, as it once was in the not too-distant past.
The religious aren't allowed to do just anything they want in the name of religious freedom. Rights are balanced. Homosexuality certainly should not automatically trump Christianity. That's been the current bad pattern of the secular governments and the new, but not finalized, worldview of so many people.