I think the hosts should pay for everything that is served, and charging guests is awkward.
But you can choose what to serve. There is nothing wrong with serving only soft drinks.
For example, I have not served any guests at my house alcohol for as long as I have owned my house, and no one ever asked for alcohol or seemed to care it was not there. My reasons were for philosophy and convenience (we don’t drink ourselves).
Once seated, wait staff can visit each table with a choice of red or white. Later, they revisit the table. Depending on your budget preference, you set how often they come by to refill. You could have beer on ice in a central spot, if you’re into bottles.
Being hospitable, yes. Imo, no one at a rehearsal dinner really needs open-ended drinking.
@younghoss - I read it that way at first too - that they were collection $$ for the couple. Upon re-read I believe the OP and her H have offered the to-be married couple either $$$ in lieu of a welcome party or the welcome party. (I was thinking like you - what? collect $$ for the couple?!)
ok I think I see it.
Not clearly written
Groom’s parents are planning the rehearsal dinner for D’s wedding at a restaurant that does not serve alcohol - not because they are cheap or anything, but because they want to share food from their heritage with the group, at a restaurant they enjoy. Problem solved for them! 
I have been to several rehearsal/welcome receptions at different weddings. I think generally speaking wine, beer and soft drinks are served. I have been to venues where someone if at a hotel restaurant in a private room for instance could walk out to the regular bar and get themselves a cocktail if they wanted. No one seems to expect an open bar at a rehearsal dinner or objects to what is being served. It is a fun evening, a way to meet the wedding party and meet the other guests.
I will be in charge of rehearsal dinner for my son’s wedding in August. I like the idea of beer, wine and soft drinks. In addition to expense, I don’t want anyone to have a hangover for the wedding. When I have parties at home we usually only serve beer and wine. The actual rehearsal is at 3:30 pm, so it will be an early dinner.
@kelsmom - most restaurants that do not serve alcohol would generally allow BYOB.
What about having a “signature cocktail” available as the only hard liquor choice
@oldfort, my D lives in PA and that was the first I’ve heard of BYOB restaurants. I’ve never heard of that in Michigan where I and @kelsmom live. They may exist but I’ve never been to one or heard of one where I live.
Additionally I have no idea which culture @kelsmom fsil is from but knowing of where she lives, he may be from a heritage that does not drink alcohol and which at restaurants which serve that community would not serve. So it may be a cultural thing also.
Around NY tri-state area, it is very expensive to get a liquor license, so there are many restaurants that do not have a liquor license. If a restaurant doesn’t have a liquor license then it is legal and free to bring your own alcohol. If a restaurant has a liquor license then they would charge a corkage fee if you should bring your own liquor (10-25/bottle). For D1’s wedding, we are considering bringing our own champagne because even with the corkage fee it would be cheaper.
Michigan does not allow BYOB in restaurants. FSIL’s culture has no issues with drinking (Arabic, but Christian) - D went to Lebanon with his family & they all enjoyed alcohol with their meals. There are not many middle eastern restaurants in our area that serve alcohol, though … not sure why (I know that many are not Muslim-run, so could serve), but maybe because licenses are expensive and difficult to obtain. There will be alcohol at the wedding reception!
Just did a wedding (with no rehearsal dinner) and IMO, the big cost factor is if the venue provides the booze and pours it (they will keep refiling a half full glass) or you buy it at your favorite discount store and they just pour it. We had about 50 people for our wedding and got two cases of white, a case of red, a case of champagne, beer and soft drinks, one big thing of vodka and mixers. Total cost was under $500. And we had over a case of leftovers.
Our vendor would not let us take home any extra bottles.
It will be simple for us, too. My parents are teetotalers for religious reasons, so we will serve no alcohol at all.
All the restaurants in tourist hotels or that cater at all to tourists in Jordan have wine. It’s often not on the menu, but if you ask they’ll tell you what they have. It’s generally wine from Lebanon and quite decent
We had two fully stocked bars at our wedding 27 years ago - I still have an unopened bottle of Nero Sambuca, and I remember thinking, “Do we need all of this stuff?” I think beer and wine are fine, and if you want to add a couple of specialty cocktails at the beginning, that will make it even nicer.
I wanted to comment about bringing alcohol to the rehearsal dinner.
Short answer, it was a disaster.
The bridal couple didn’t want me to bring a ton of alcohol because they didn’t want everyone hung over on the day of the wedding. So for 19 people I brought 4 bottles of white, 3 bottles of red, 4 large cans of hard cider (3.5 glasses per can). A case of beer and soft drinks.
Firstly, we took a wrong turn going to the site and were 45 minutes late to the rehearsal dinner. I packed a wine opener but it got put in the wrong place and didn’t make it to the dinner (we had tons of stuff to bring that were going to 3 different places).
The bridal party wanted to have fun. When we got there 45 minutes late all the white wine was pretty much gone and most of the cider. None of the red was being drunk and none of the beer. My friends all drink red wine and beer. Not this crowd.
So don’t listen to me. I can laugh about it now but it was pretty much a big fail. :))
DH and I paid our entire wedding bill ourselves, including the rehearsal dinner, which included the bridal party of 10 (ncluding both of us), a few of them had dates, plus both parents and her beloved aunt/uncle who travelled far and stayed overnight. The priest who married us was a longtime family friend of my mom’s since they were neighbors in grade school. The parish rules dictated that the priests were not supposed to come to the wedding receptions - so as not to cause hard feelings if they came to one, not another, etc. So we were pleasantly surprised when Father came to join us for the rehearsal dinner. We were even more surprised when Father told us he was picking up the bar tab - the story he told us was that an anonymous parishioner had recently bequeathed a small sum that should be used for special celebratory occasions.