One way to set different alpha values based on smoke = Yes/No would to use the below code. You can set different colors and alpha as required.
import seaborn as sns
tips = sns.load_dataset("tips")
ax=sns.stripplot(x="day", y="total_bill", data=tips[tips.smoker == "Yes"], alpha = 0.3, color = 'darkgreen', edgecolor='black', linewidth=1)
sns.stripplot(x="day", y="total_bill", data=tips[tips.smoker == "No"], alpha = 0.3, color = 'red', edgecolor='black', linewidth=1)
Plot

EDIT
To set the colors directly, you can set your custom palette as below and then use smoker as hue.
# Create an array with the colors you want to use
colors = ["red", "darkgreen"]
# Set your custom color palette
sns.set_palette(sns.color_palette(colors))
#Use hue for smoker to differentiate colors
sns.stripplot(x="day", y="total_bill", data=tips, alpha = 0.3, hue = "smoker", edgecolor='black', linewidth=1)
IF your requirement is that HAVE to use to_rgba(), then you can set it in colors and keep the alpha here as well. This is the other code...
# Create an array with the colors you want to use
colors = [to_rgba("red", 0.3), to_rgba("darkgreen", 0.3)]
# Set your custom color palette
sns.set_palette(sns.color_palette(colors))
#Use hue for smoker to differentiate colors
sns.stripplot(x="day", y="total_bill", data=tips, hue = "smoker", edgecolor='black', linewidth=1)
In both cases, plot will be as below.

New Requirement
As you mentioned in the update, you are ok with the colors from scatter plot. You can write a small function to add jitter to your figure, which will achieve what you are looking for. See the update to your scatterplot code below to achieve what you are looking for.
import seaborn as sns
from matplotlib.colors import to_rgba
tips = sns.load_dataset("tips")
color_dict = {'Yes': to_rgba('darkgreen', 0.1), 'No': to_rgba('red', 0.1)}
#The days are strings, convert to numbers for plotting
Numday = {'Thur': 1, 'Fri': 2, 'Sat': 3, 'Sun' : 4}
def addJitter(x): ##Function to add jitter. Adjust numbers to make it thick/thin
return x + random.uniform(0, .3) -.15
## Convert day -> Numday which is a different number for each day
tips['numDays'] = tips['day'].astype("string").apply(lambda x: numDays[x])
## Use jitter function to add jitter to each numDays
tips['jitter'] = tips['numDays'].apply(lambda x: addJitter(x))
sns.scatterplot(x= tips.jitter, y=tips.total_bill, hue = tips.smoker, palette=color_dict, edgecolor='black', linewidth=1)
## You will need to reset the x-axis to show the day
plt.xticks([1,2,3,4])
plt.gca().set_xticklabels(['Thur', 'Fri', 'Sat', 'Sun'])
