It's very common for people faced with one form of discrimination to say something like "you wouldn't say/do that about/to [other group]". In practice, the other form of discrimination used in the comparison is almost always racism. Here's a recent example from Stonewall UK (The F-Word have a screenshot and some more context).
It's a terrible argument.
The basic assumption behind the argument is that racism is taken more seriously than homophobia (since the recent example is those two, I'll use them in this post, but this all generalises to any form of discrimination). The evidence presented for this is generally that the use of racial slurs is condemned, but the use of homophobic slurs is not condemned (or at least not as strongly)
Oppression Olympics
The first thing wrong with this is the standard "Oppression Olympics" problem. The nature of oppression means that it's not meaningful to ask which is worse. This does not mean that in a particular society all oppressions are equally bad, just that they're all linked together in such a complex way that even determining where one sort begins is tricky. Weighing up the effects across society of two sorts to determine which is "worse" becomes impossible. Even if it were possible, there wouldn't be a lot of point to doing so - once you know "severe, sometimes fatal", it's usually a waste of time to go around putting more precise numbers on it.
When you go from effects on society to effects on the individuals that make up society, the "which is worse" question gets even more absurd.
The line of argument of course generally ends up erasing people who are both BAME and LGB - if the response to "you wouldn't do that to a black person" can be "but I just did" the argument clearly doesn't work, but often the people using the argument assume that people can only be one or the other.
An argument that generalises to "You wouldn't discriminate on one ground in exactly the same way that you discriminate on other grounds" might be true but it's not particularly useful, since of course there are differences between oppressions beyond exactly which part of humanity is on the sharp end.
Only true if it isn't
A second problem is that the argument relies for its effectiveness on the basic assumption being true, but relies for not being obviously absurd on the basic assumption being false. Let's swap out racism for something that really is generally considered unacceptable in this country. "You wouldn't steal from a charity, so why do you use homophobic slurs?" or "You wouldn't insult people for their eye colour, so why do it for their sexuality?"
Or keep it as racism, but use an archaic slur - "You wouldn't say [obscure 15th century racial slur], so why do you use [homophobic slur]". It still doesn't work as an argument, because the whole force of the argument is in the instant shock value and familiarity of the racist slur.
But if the racist slur actually has shock value, then that's because racism is a problem. And if racism's a problem (which it is), the first half of the argument that "you wouldn't use a racist slur" isn't actually generally true. And, of course, using a racist slur purely for its shock value is exactly the sort of behaviour the argument is saying is unacceptable.
It's right about the "unacceptable" bit, though it'll be a while before that's generally agreed on.
A low standard
A third problem is that since racism is still a serious problem within society regardless of the exact severities of its various manifestations. A campaigner against homophobia really does not want to have "Why don't you discriminate against us more like you discriminate against BAME people" as their argument.
This brings out the assumption behind the argument - that because you "can't say X any more", racism is over or at least substantially weakened. It's not a good claim.
