This is Stonewall's definition of homosexual:
Homosexual
This might be considered a more medical term used to describe someone who has an emotional, romantic and/or sexual orientation towards someone of the same gender. The term ‘gay’ is now more generally used.
This is the definition of homophobia on Wikipedia:
Homophobia encompasses a range of negative attitudes and feelings toward homosexuality or people who are identified or perceived as being lesbian, gay, bisexual or transgender (LGBT). It has been defined as contempt, prejudice, aversion, hatred or antipathy, may be based on irrational fear and ignorance, and is often related to religious beliefs.
Homophobia is observable in critical and hostile behavior such as discrimination and violence on the basis of sexual orientations that are non-heterosexual. Recognized types of homophobia include institutionalized homophobia, e.g. religious homophobia and state-sponsored homophobia, and internalized homophobia, experienced by people who have same-sex attractions, regardless of how they identify.
Stonewall's definition of homosexual is institutionally homophobic as it is based on gender, therefore how people identify, rather than their sex.
This is why the LGB Alliance was set up.
Wearing a t-shirt that says LGB Alliance on it, is a statement of this.
Those who believe in the Stonewall definition are homophobic and do not like being called out on it.
Saying that this is in anyway being like a nazi is pretty special in this context. I have to question anyone who defends the Stonewall definition. Especially if they are prattling on about how it's like a nazi to point out institutionalised and internalised homophobia.