My 17 year old daughter has CP, walks with crutches and, occasionally, uses a wheelchair. She isn’t here right now (she’s at school), but I feel I can speak for her in these matters.
Offering assistance: Please do. It’s perfectly acceptable to hold a door for anyone who looks like they need it – a mom with a stroller, a person with their arms full, etc. Doe can open doors herself, but it’s a bit of a struggle in her chair and even on her crutches, if the door is heavy. She’s always happy for the assistance. Likewise with an offer to get an item off a tall shelf. Doe is very short (4’9") and also has some range of motion problems that make it difficult for her to reach up, even when she’s on crutches. In the 'chair it’s even harder. If you offer to help her reach something it saves her a trip to find a store clerk, which is much appreciated. We consider these kinds of assisting to be simple politeness – as you say, these are things you might help an ablebodied person with also. Slightly different are situations in which you have to touch a person’s 'chair or crutch to help them. As has been said, a wheelchair or crutch should be considered part of the body when it comes to touching. So, for instance, if you noticed my daughter struggling to move her chair out of a tight space, you should ask her if she would like some help and, if she says she would, specifically ask if you may move her chair – being careful to let her know just before you actually move it, so she can get her hands free. Or, if her crutches are out of her reach, don’t just hand them to her, ASK if she would like you to get them. And, of course, take no for an answer. If it were Doe, she’d be happy for the help, but some people just prefer to do things themselves.
Major pet peeves: Doe hates being spoken to as if she were a child. This is partly because she is so small, I suppose, but also it’s the crutches/ wheelchair. Some people do assume she is retarded because she can’t walk. Worse are people who don’t speak to her at all, but instead address her through me (or her brother or Dad or friend). She also really hates to be patronized – she has actually had people (strangers!) say things like, “You’re my hero!” or “I’m praying for you!” She hates that. Also, she hates the occasional pitying look or overheard pitiful comment – that “Poor soul!” really gets on her nerves. And she hates it when people freak out if she falls. Falling occasionally is common when you use crutches. In fact, part of learning to use crutches is learning to fall. But people just come unglued when she falls. If you see someone on crutches fall, do watch to be sure they’re OK, but don’t have a conniption or make a big fuss. Don’t just grab them, unasked, and yank them upright (Doe has had people do this!). Ask if they need help, and if they do, ask how you can help. When Doe falls, she usually wants to stand up again by herself, but appreciates any help gathering dropped items. Sometimes, if the floor was slippery, she might need help standing and want your arm getting past the slick place. She’ll know what kind of help she needs, so just ask her if you can help, then follow her instructions.
Finally, please don’t let those rude people – and disabled people can be rude, just the same as ablebodied people – make you second guess yourself. A person who responds to a polite, well-meant offer of assistance with irritation is being rude. Period.