I grew up on Emily Post & Miss Manners & according to them there is nothing wrong with inviting people to the wedding & not the reception. If you're a member of a church & the wedding is held at the church, then any member is allowed to attend the wedding unless you have an usher at the door with a list. And some churchs hold hundreds of people but you may not want (or can't afford) that many at the reception. But wedding invitations should not have directions to the reception if the person isn't invited. And they certainly shouldn't take your gift & then turn you away.
Also, where I grew up people didn't bring gifts to the wedding/receptions so if you weren't invited to a shower you sent your gift to the mother of the bride's house or to the bride if she lived somewhere else. And family NEVER threw any kind of shower or gift grab & the happy couple NEVER even implied they would like money. (If family threw a shower then ONLY family were invited, otherwise it was considered tacky.) The bridesmaids were supposed to throw one shower, usually a lingerie shower, & usually friends of the parents would throw others.
Re the plus one, when I was a single girl I expected to be able to bring a date to the reception unless it was a very small one held in someone's home. But of course if the invitation didn't say + 1 then I could either choose not to go or to go alone. Etiquette sure has changed a lot.