We don’t genuflect to the tabernacle. When the Blessed Sacrament is present in the tabernacle, which is usually signified by a lit sanctuary light near it, then we genuflect before the Blessed Sacrament.
When passing before a dedicated altar, we show reverence with a profound bow, solemnly bending the upper body from the waist (as opposed to a simple bow, which is a solemn bow of the head).
When the Blessed Sacrament is not in a tabernacle immediately behind the altar, in which case a genuflection is sufficient to show reverence for both, then the reverence proper to each is shown when one passes before each. Even if the Blessed Sacrament is not held in repose, it is proper to bow to the altar.
What I don’t know is whether a fixed altar that is used for Mass but is not dedicated solely to Catholic worship is reverenced when the altar is not in use for Catholic services. I know that a table that has been used in the past for Mass does not receive that reverence, as it is not a dedicated altar. My impression is that an altar is only dedicated if it is truly going to be reserved for the Sacrifice of the Mass alone, and if it is not, it is treated as one would treat a table used for a Mass. The table has to be of noble material, it may even look like any other altar, but it is not consecrated by use only. (If it is dedicated, it should not be used for anything else whatsoever, including non-Catholic Christian liturgies.) Likewise with a sanctuary that is not dedicated for Catholic liturgy. A gym that is sometimes used for Mass doesn’t become a church.
But with regards to fixed altars in chapels that other groups are allowed to use, that is a guess. If the altar is dedicated, it shouldn’t be used for anything else. That doesn’t mean it isn’t.
Bows and genuflection aside, I think that maintaining a quiet proper to a place of prayer and an attitude of respect for the use to which the space is dedicated is admirable even in a Protestant or interdenominational church, whether or not quiet is widely observed. It does no disservice to Catholic churches to treat every church as a place set aside for the quiet voice of the Holy Spirit. On the contrary, I think that it reflects well on the Catholic Church if Catholics show the respect of maintaining a prayerful attitude in every space set aside for prayer. Neither does it hurt to make a Sign of the Cross to remind yourself of your baptism when you enter and leave, even if there is no altar to bow to and the Blessed Sacrament isn’t present, as the gesture of the Sign of the Cross is proper throughout our days, inside church and out.