All of this needs to be worked out before extending the invitation, or allowing it to be accepted. The rabbi and priest need to walk the church and agree on what is and isn’t allowed or acceptable for both sides. Of course, the parish should furnish a staffmember who is fully aware of the agreements to be on hand at all times that non-parishioners are using the church, to make sure the agreements have been correctly understood and followed in real time. I’m sure that would be expected.
As for covering the statues and crucifixes, my home parish used to do the same on Good Friday. We had purple coverings for all of them. It isn’t inherently disrespectful. It is actually in accordance with what is going to be going on in the space. Likewise, the altar can be covered or stripped, someone can be on hand to make sure it is not used in any way whatsoever, and of course the Blessed Sacrament must be removed to a different location, just as it is for Good Friday. I would find all of this as much of a reverence to our beliefs as to theirs. Certainly, if we were to use a synagogue and they removed the Torah scrolls, I would take that as a show of respect for the Torah, and not just something to keep us from feeling uncomfortable.
This is not an ideal situation, but let us hope that some religious group that doesn’t believe in the Mass would allow us to use their space, if we were flooded out, burned out, couldn’t afford a big enough sanctuary yet, etc.
OTOH, if a congregation isn’t generous enough or is too easily scandalized to manage this, then that has to be recognized. I wouldn’t expect a synagogue to welcome Catholics if it was going to cause a stir in their congregation. It is like temporarily moving into somebody’s home. If the guests are not joining the family, but are essentially using the home as their own private retreat, as they might if they were burned out and the host family moved in with relatives until the burned-out family could rebuild, then the whole family really should be comfortable with the arrangement, even the ones who might not normally have a say about who is and isn’t welcomed as a guest at the family table.
Jews do not have an obligation to go to synagogue every week, but they are obliged to attend the High Holy Day services. A congregation that can get by with a modest space the rest of the year can find themselves beyond bursting during High Holy Days. Every congregation would like to meet in their own synagogue, but sometimes building a sufficiently big space is just not possible.
I think this is an opportunity to “welcome all as Christ” myself. I think it reflects badly on this love of both brother and enemy that we’d like to be so proud of, if we are not even hospitable, but that is just me. The main thing, though, is to either be fully hospitable, or else not at all. You can’t welcome somebody for High Holy Days and expect them to be pseudo-Catholic for it. That does more harm than good.