I actually think it would be just the opposite. Aerith has lived her entire life knowing she would be lonely. She reads people well (although reacting to it, especially with people she isn't close to, is difficult for her) and she has a good understanding of the kind of person Cloud is and what he needs/wants. I would think it would be easier for him to open up to her because she probably wouldn't push so hard for him to open up.
Look at the difference in the two girls' behaviors in Kingdom Hearts. It may not be canon, but it's still a reflection on their relationships with Cloud.
I don't think Kingdom Hearts Aerith's actions are always a good reflection on how Final Fantasy Aerith would act. The scene with Cloud in KH2 is a total reverse on what FF Aerith does whenever Sephiroth is involved. KH Aerith says she'll stay here and cheer for him. FF Aerith runs off to stop Sephiroth herself and tells
Cloud to stay there. And it's not just a one time thing! Case of Lifestream White has her trying to tackle the problem herself until she's overwhelmed before searching for other spirits to help her, and then when
that fails, in the middle of an epidemic that may come to threaten the Planet, she waffles over if and how to tell Cloud that shit's going down to get his help.
Both Aeriths end up being cheerleaders for Cloud, but their attitudes toward it pretty different. If FF Aerith had a physical body during AC, I doubt she'd be cheerleading; she'd be busy putting that body out on the frontline and possibly giving Cloud a panic attack ("Hey, because of my heritage there's this special thing only I can do to help against the remnants, be back later!" "
WHAT?!") on top of everything else going on.
As you said, Aerith has lived her entire life knowing she would be lonely... and this is one of the key differences between her and KH Aerith, who as far as we know has at least had the rest of the Traverse Town crew for the past 9 years and doesn't have any unique talents to hide or be persecuted for. It's exactly the loneliness that I think might cause trouble for FF Aerith in a relationship or in a family. She didn't tell Zack certain things that kiiiinda were relevant to him, since he worked for the company trying to kidnap her, she's run off from home, she's stubborn. Which she kind of needs to be, since Tseng keeps trying to convince her to go back to Badtouch Labs--she needs to look out for her own interests--but she's stubborn enough that her mom points it out about her, doesn't even try arguing with her on things, then sneaks around Cloud trying to leave, aaand she never does actually listen to Cloud when he tells her not to do something dangerous.
It just seems like if they ever got into a real argument, Aerith would be frustrating to deal with.
Does Tifa push too hard for Cloud to open up? Yeah, she does ask about him, but it never really seemed excessive to me.