What is the difference between someone saying "Homosexuals should be executed" and "Paedophiles should be executed"?

Or even restoring the death penalty?

http://www.bnp.org.uk/news/national/sign-petition-restore-capital-punishment

None, I would suggest, since they are only proposing a change in the law.

Since they are expressing a political opinion, someone (such as a homosexual or a paedophile or a murderer of children or police officers) who holds the opposite view is bound to be offended.

So, while I profoundly disagree with the female student who declared that it would be right to execute homosexuals, I would defend her right to say it.

The Middle Eastern studies undergraduate who secretly filmed the discussion asked a member of the society whether, “in the Islamic society in which you strive for,” they would “feel comfortable, personally and morally, to kill a gay man".

The female student replied: "Absolutely," and described homosexuality as an "atrocity, because it goes against what God says".

The student was also asked if she, in her "ideal" Islamic state, would feel confident to kill a man if he "did something as com­pletely innocent as kiss another man outside the Students’ Union," to which she replied: "Yeah, abso­lutely ... "

http://www.huffingtonpost.co.uk/2013/02/25/manchester-student-society-kill-homosexuals-shuts_n_2764273.html

I would also point out to her that the Koran does not in any case says homosexuals should be executed, it only says punish them.  They could be fined, or be lashed 100 times just like those who are guilty of fornication or adultery, or God could ordain another way.

All the Abrahamic faiths are "homophobic" in any case.

Koran:

4:15.

If any of your women
Are guilty of lewdness,
Take the evidence of four
(Reliable) witnesses from amongst you
Against them; and if they testify,
Confine them to houses until
Death do claim them,
Or God ordain for them
Some (other) way. 

4:16.

If two men among you
Are guilty of lewdness,
Punish them both.
If they repent and amend,
Leave them alone; for God
Is Oft-returning, Most Merciful.

http://en.wikipedia.org/wiki/The_Bible_and_homosexuality

Old Testament:

Leviticus 18 and 20
Chapters 18 and 20 of Leviticus, which form part of the Holiness code, contain the following verses:
22 Do not have sexual relations with a man as one does with a woman; that is detestable. (Leviticus 18:22 NIV)
13 “‘If a man has sexual relations with a man as one does with a woman, both of them have done what is detestable. They are to be put to death; their blood will be on their own heads. (Leviticus 20:13 NIV)

New Testament:

Romans 1
“ 26 Because of this, God gave them over to shameful lusts. Even their women exchanged natural sexual relations for unnatural ones. 27 In the same way the men also abandoned natural relations with women and were inflamed with lust for one another. Men committed shameful acts with other men, and received in themselves the due penalty for their error.(Romans 1:26-27 NIV)

"Phobia" means an irrational hatred and fear of something.

Is it ever irrational to hate and fear those who promote homosexuality?