I was asked to come and even invite others to join a musical prayer service hosted by a conservative temple. Can I attend?
This is quite a serious issue, regardless of the venue.
Anything which can be interpreted in any way as a tacit approval of the movement or temple is unacceptable. This is in contrast to the individuals where tolerance and often even acceptance is encouraged.
See אגרות קודש יד, ה׳קסא.