Do you get the feeling that you're not really welcome, or at the very least, you're pawns to get the Jews back and will thereafter be discarded?
Thanks
What good is an answer that isn't pedantic? Don't answer that. Your question cannot be answered without reference to the Reformation and schism in the church.
Jews are hostages in a debate with Christians, because they have the most to lose in a conversation about the Bible, it being theirs. They are the ones with their necks sticking out if the Bible is used for ill purposes. Whenever someone criticizes Christians, Jews often get included. So, no we are not pawns of the Jews. They are our hostages for the time being. They are manipulated by seemingly arbitrary winds of change.
The Roman church (pre-Anglican) resisted allowing the Bible be translated into English, because the church felt that people would totally misunderstand it without learning the original languages and without some education. The church was correct about that, although the church organization spread harmful superstitions and was generally very disappointing, badly managed and corrupted by politics. It lost the good faith of many people. Some people got upset enough about the general state of ignorance of the populace and of the clergy that they illegally translated the Bible, thus liberating it and placing it into the hands of ignorant English readers. The idea was to force the church to reform and give people a chance which partially worked. Partially it was like exploding a bomb, because lots of Christians got hurt although some reform did result. A lot of Jews got hurt as a result, too.
As for your question about getting the Jews back into Israel and whether we are being manipulated, no; but we did want them in Israel yes although not until after the Reformation and for unanticipated reasons. Actually the events leading to Christians wanting to re-create Israel were quite unanticipated. My understanding is that this came about because the Bible got printed in English, then distributed in mostly rural USA. After that many Christians in USA, mostly poor folks, began to focus on literal interpretations of the Bible, we began to hire our own ministers who preached what we wanted to hear. We rejected previous institutions and started over. We wanted to hear that Jesus would fly down from heaven someday, save everyone from troubles and end all suffering and woe, so that was what was preached. We also began to speculate that in order for Jesus to fly down, Israel would have to be created first.
There is a craze among those Christians who expect Jesus to literally fly down from heaven barefoot that Israel must become a country before he does; but its not originally the mission of the church nor of Christians. 'Scripturally' there is a New Jerusalem from heaven which will be in people through the church, and the church is fulfilling the role of Christ on Earth, already. We don't need Jews to live in Isreal or need Jesus to fly down barefoot in a robe to alight upon the Mt. of Olives., but in recent centuries protestants have started to think that we do as a result of a Bible printed in English and a complete rejection of the Roman church including its scholarship. (A very much deserved rejection. There was no avoiding it.)
The formation of Israel has been a favorite with among various reformed Christians since about three centuries ago. You can read about various ideas of what political events might bring it to pass in all kinds of old protestant publications. The formation of Israel is looked at as an extremely exciting and wonderful prospect. In fact to me it feels likely though I have no evidence that it was protestant Christians who managed somehow to get Israel to become a country, using the horror of WWII as an opportunity to make it happen. We brought the subject up frequently for well over a hundred years and envisioned it; thus creating the conditions for it to happen I think. Jews did not put us up to it and were not really that interested in forming a country in old Israel territory, not until Theodore Herzl; but who do you think got Herzl to be interested? He was known for interacting with protestants in Germany, and he was the founder of modern Zionism -- but not really. Actually protestant Christians are, and we continue to be its primary strength. Many, many of us are still hoping Jesus will fly down and alight on the Mt., barefoot.