-In the UK, discrimination based on sexual orientation is illegal (Equalities Act 2010)
-The UN's Universal Declaration of Human Rights gives the right to love whoever you want.
-As the Utilitarian philosopher Peter Singer puts it, "If an activity brings satisfaction to those who take part in it and harms no one, it can't be immoral" - this is a view most non-religious people, certainly Utilitarians, probably hold.
-However, because of the influence the church and religion has had on British culture, even people who are not religious may still hold negative views towards people who are gay. In 2018-2019, there were nearly 15k hate crimes based on someone's sexuality recorded in the UK (https://www.hrw.org/news/2019/10/23/...ocking-reading)
-In certain parts of the world, non-religious people may view homosexuality negatively for reasons other than religion. Eg. China is officially atheist as a country, but gay people are treated poorly because homosexuality is not seen to conform with China's cultural/family values.
-Some people who are not religious may be supportive of homosexuality but not supportive of the LGBTQ+ community for reasons unrelated to homosexuality eg. they don't support gender reassignment surgeries for children
It has been theorised that in-utero exposure to high levels of testosterone may cause homosexuality.