The two situations are different:
Your first situation is a personal conviction thing.... while there
is no obvious reason why a Christian cannot work in a spa, some
Christians may not make this career choice as it may be seen as a
poor testimony or that the career may open to unnecessary
temptations. So the issue really is what you, as an individual
think.
The second situation is a issue with the employment people. There
is really no such thing as an equal rights employment. Each
organisation/company will have their own specifications as to what
they want in an employee. Perhaps Singapore Pools feel that there
is a conflict of interest in a Christian working for a gambling
organisation, and such an employee may also be seen as a threat if
this employee become extremist in their belief.
My church has ladies who own spas and work in spas and hairdressing
salons. Absolutely nothing wrong with it.... especially when these
business are completely legit.