I too read Bhagawad Gita and I agree with what you quoted from Gita.
If the Lord does not hate anyone, why did he ask Pandavas to kill Kauravas? There is a reason, right? Kauravas did not respond favourably to many of his peace attempts and they were bad. So, he wanted them to be killed, even though "none is hated by me".
Similarly, just because the Lord does not hate anyone, it does not mean that everyone should be allowed inside a temple. It is a different matter.
For the sake of arguing, will everyone be allowed to enter heaven? No. Only those who do good deeds will be allowed to enter heaven.
Similarly, a temple has its own rules.
A temple is not merely a cement building, where a stone is decorated with flowers and strange Samskrit sounds are made.
It has much more to it.
Just as you read Bhagawad Gita, I suggest you also read Osho's (Rajaneesh of Pune) book called "Hidden Mysteries", which explains some of the secrets of majestic temples and explains why temples are the way they are.
Before I read that book by Osho, I too thought that a temple is merely a brick building and visiting a temple is a routine ritual.
There is very little all of us know about Hinduism.
Let us have an open mind. Let us have the humility to not question some of the things.
