Conversion in allowed case by case, i know families that have welcomed non muslims/new converts with open arms and some families see it as a big shame and dont allow it. I would welcome it as its a good thing to convert a non muslim to islam.
ShelBel write: Surely one should marry a person who will look after her, even if hes not muslim, i know so many failed muslim marriages in UK because the muslim man cannot stand westernised women.
3.28] Let not the believers take the unbelievers for friends rather than believers; and whoever does this, he shall have nothing of (the guardianship of) Allah, but you should guard yourselves against them, guarding carefully; and Allah makes you cautious of (retribution from) Himself; and to Allah is the eventual coming.
[3.118] O you who believe! do not take for intimate friends from among others than your own people; they do not fall short of inflicting loss upon you; they love what distresses you; vehement hatred has already appeared from out of their mouths, and what their breasts conceal is greater still; indeed, We have made the communications clear to you, if you will understand.
It is not to judge you but I think you should read Quran. Allah doesnot want believers to be with infidels. last thing He would want is for a believing woman to marry a non-believer. And if you dont agree with this then your weak in eeman or you are a non-believer acting like a muslim which is worse. May Allah protect us from the Munafiqueen and all else evil.