can a person be considered open minded if he/she accept LGBT but can not accept the fact that his own son is gay?

Possibly.  That scenario suggests that he/she is acting out things that don't have directly to do with the acceptability of homosexuality.  For example, a father might have an emotional difficulty with the amount of everyday defiance and resistance he gets from his teenaged son - and so his reaction might be about THAT rather that about his son's homosexuality, per se.

A mother might be overwhelmed with anxiety about her standing among her peers at church - and so her reaction might be about THAT rather than about her daughter's homosexuality, per se.

Openness to LGBT in principle is one thing, and one's relationship with family members or with the community are different, separate things that can complicate one's emotions.  This is particularly true if the parent imagines the child's homosexuality as a "bad decision" or a "phase".

Think about the possibility that Dad could be subconsciously dealing with such distractions - like the fact that some of his peers will be talking behind his back about how HE must be "to blame for is gay son", or perhaps that he must be a "closet gay" himself.

Or consider that he might feel that homosexuality leads to bad results, like AIDS, or social ostracism, or poor financial security, or drug abuse, or a broken heart, and solitude in old age.  (We know these are not inevitable results of homosexuality, but perhaps HE believes they are.)  So, while he might believe that people who are LGBT are headed toward misery and also believes that doesn't mean they should be discriminated against (that is, he's "open-minded" in principle) - he is naturally unwilling to accept such misery should befall one of the people he loves.

That would be a matter of a deep-seated misunderstanding on his part, rather than a hypocritical bias against LGBT offspring.

I appreciate big ol pickup trucks, tuners, cars bouncing on hydros and even undesirable cars fixed up. Classic cars and new cars. Electric, gas and diesel. Sleepers are awesome, cars converted into 4x4 are great. I am open minded to the whole craft, the art. Tractors are great, I have an old farm tractor and nobody gets to use it. Ford vs Chevy, who cares childish. I ride motorcycle even. Yet I don't accept my kids and wife driving cars that are not full of modern saftey equipment. You can call it what you wish. Double standard, lacking open mindedness, hate or whatever. As we both know nobody gets to define themselves, others will define me as they see fit. I could imagine a gay person not wanting their child to be gay. I don't need to know why to accept their right to feel that way. So, it's complicated, like most things.

No. If they're okay with gay men only in the abstract, but not when it's someone they care about, they're not really okay with gay men--no matter what they tell themselves.

No. Thats shallow and selfish