Reading the OP, I see that Rabbi of Crawley begins “we as Jews”. Can he say what “we” “must” do? Is he speaking for All Jews? Torah observant Jews? Chareidi Jews? Secular Jews?
It is admirable that he condemns the murder of Shira Banki. It is admirable that he seeks to maintain the kedusha of Yerushalayim. I question the wisdom of having such a parade in the middle of or the religious parts of the city. It is also the parade aspect that bothers me, and if anyone, gay or straight, wants to have a parade celebrating hedonism that includes anything more than clothed people with flags and banners on my street, let alone Yerushalayim, I would be quick to object.
Where I don’t object is the demonstration, the political element of this. In a liberal democracy, if you want to safeguard your own parochial rights, you have to recognize the societal rights of others, no matter how distinct they are from you. Otherwise, you are breaking the very foundations of tolerance that allow you to thrive, in the US, Europe, Israel etc. The gay “community” does suffer discrimination, as do other “communities”, and they have a right to demonstrate about these grievances too.
Hillel Hazaken said “what is hateful to you, don’t do to others” If you would be upset because someone didn’t allow you to demonstrate for something you found important but he found offensive, you would be incensed. Hillel tells you not to be a hypocrite, and he doesn’t qualify the statement with any conditions.
Until and unless the State of Israel determines to be a state ruled by Halacha exclusively, They would seem to be within the law. If you don’t like the law, work to change it. But violate it at your peril.