No. It will make people much less unique and won't really stop a lot of the problems anyways. Many of the problems has to do with clashing of cultures.
Even if people became to blend into one race, doesn't mean cultures will blend. While most populations aren't truly homogeneous, there has always been many different cultures and people were never really a collective bunch. Even countries with genetic similarities can differ greatly.
Also genetics are a funny thing and what is passed down can be random. People get 50% of their genetics from each parent, you just don't know which of those genetics will be passed down. There are no guarantees. As long as you can carry the genes, it really won't stop people from getting different hair, eye or skin color as well as other features. A lot it had to do with mutations and I am sure genes will mutate once again in the future as well (especially depending ones environment).
While I don't think it should be forbidden per say (people should marry and be with who they love and the dominate culture that they follow and practice should be of the country that they live in), I do think that it should never be forced (which why I dislike the whole migrate crisis). Forcing mixing never work; just look at the mess some countries are in now? Even other Asian, African and European countries don't get along; much less adding people from extremely different background that are completely foreign.