What are the effects if a mother refuses to accept her son is gay?

They are rather wide ranging possible outcomes in such a situation. And let's be a little wider in scope and just say a parent or parents and a child, son or daughter since the same effects would apply to any combination of these.

One possible outcome may be that the child distances him or herself from the parent because he feels they aren't respecting him yet will still act somewhat socially responsible with them. There is likely a cold undercurrent to this sort of relation.

Or the child, if old enough, could simply stop talking to them completely and cut them out of his/her life.

Another outcome could be that the child will feel ostracized and in order to please the parent(s) will attempt to downplay or even quash his real feelings in order to fit into their pre-conceived view of what he/she should be. This will usually end up a very bad situation where there is likely some serious self-worth and self-disgust issues that will grow out of this misguided attempt to get back and deep into the closet in order to please someone else.

Yet another could be suicide if the child feels that his own parent doesn't care for him; he may feel like he is an error, a problem and/or an embarrassment and become depressed while making a point of not talking to anyone about it due to the shame brought on by the parent's disapproval.

When he feels like he's alone in the world and rejected by his own parents as bad, sick and wrong at a time when he really needs their support and unconditional love the most, that and the high pressure from outside factors (community, church, etc.) who may also be painting a picture of "homos" as disgusting people not worthy of love or the slightest affection, a young child may see suicide as the best way out of a hate filled life.

Of course, these ar just a few potential outcomes, every single situation is different and unique; the outcome will be specific to the dynamics and personalities involved.

To this parent I would hugely recommend they get past their personal problems with gay people - because that's the actual problem, not the gay child - and contact a nearby chapter of PFLAG (PFLAG.org) to discuss their situation with other parents who've gone through it before.