When they say birth control effects muscle growth does that mean you cannot build muscle while on them or it means that you will have to workout longer time to build ?

Hormonal contraceptives (especially progestin based ones) can lead to 40% decreased muscle building capacity. This is caused by two factors: Increased cortisol results in more muscle breakdown, and lower levels of anabolic steroids leads to less muscle development (despite workout time). The best option for an athlete worried about this is to use non hormonal contraceptives such as a copper IUD.