Can my employer require me to compete in a ‘Draft’ for my schedule?

It normally would be legal: highly unusual, unprofessional, arguably improper and very likely stupid, but legal. That's because employment is, in the absence of a written employment contract to the contrary, "employment at will," which means, among other things, that an employer is not obligated to schedule staff and can set any rules for employees/employment which are not inherently illegal--and doing an offsite draft or meeting at a bar is not inherently illegal.
However, you raise a religous accommodation issue: the law prevents employers from discriminating against people due to their religion and must make "reasonable"--not too expensive or disruptive--accommodations to religious beliefs. If being in a bar (not: it would have to be simply being in a bar which violates your faith, since you can be in a bar and not drink, so a religious prohibition against consumming alcohol would not be a sufficient reason, since you'd have the option to go and order coffee, water, soda, etc.) is against your believes, and/or if is the only time your services are held (i.e. it's not the case that you could, for example, go to, say,  services at some different time instead), then this may well be religious harassmant or discrimination and you may be entitled to an accommodation. If you believe this is the case, contact the federal EEOC about filing a complaint.