Is participating in an Islamic competition with the intention of obtaining money considered shirk for the participant, and would the resulting money be unlawful?

Religious competitions are not purely acts of worship for which a person would be sinful if their intention was mixed with polytheism. Rather, they are among the actions primarily designed for worldly sustenance and benefits, to which the meaning of worship was then attached. The difference between them and pure acts of worship, such as prayer and fasting, is that ostentation (riya') in pure acts of worship makes the doer sinful, whereas it does not make one sinful in competitions, although the reward for them is only attained through a good intention.