Is placing for-profit advertisements on a religious da'wah website—after it had been purely for the sake of Allah—considered a lack of sincerity, and does the owner's reward for it become void because of these advertisements?

If you intend for your da'wah (Islamic propagation) website to be a waqf (endowment), then it is considered an endowment, and it is not permissible for you to earn money from it, because it ceased to be your property once it was endowed. However, if you did not intend it to be a waqf, but rather intended to benefit people through it as an act of drawing closer to Allah, then there is no harm in you profiting from the website's advertisements, provided that these advertisements do not negatively affect people's benefit from the website in its da'wah capacity.